Gargamel

Steam access wasn't introduced to KSP until ~.21 ish.    Unless you already own a copy of a game version from between ~.13 and 1.0, it is illegal to obtain one.   On both the KSP store and Steam, Squad maintains the most stable release of (almost?) each major update from 1.x on, so you can get those.  
Read through this thread, and some of the threads it links, to find more info.
 

It will probably run slow, but yes, I think your machine can handle the stock game.   Mods might be another question, as you will be limited by RAM.  But to be honest, your machine is on the very low end of what can run KSP.  Don't expect high frame rates or fast loading times (I used to have 20-30 minutes waits just to load the game), but it should be playable. 

It will probably run slow, but yes, I think your machine can handle the stock game.   Mods might be another question, as you will be limited by RAM.  But to be honest, your machine is on the very low end of what can run KSP.  Don't expect high frame rates or fast loading times (I used to have 20-30 minutes waits just to load the game), but it should be playable. 

Welcome to the Forums @RoM_Axion.  We ask that you please host a log file on a service like Google Drive or Dropbox and link it here.   Large walls of text can make it hard to read on some platforms. 
But here's your main issue.   4 GB is really tight for KSP to run on.   It's doable, but tight.   Shut down anything else you can that might be running in the background to free up RAM. 
 

Try changing the resolution till it fits and you're happy?

Isn't there a minimum experience level to use chutes?   I don't use them enough to know. 

Is this a career game and have you unlocked the tier 2+ tracking station?   That is required for maneuver node editing. 
 

No reason it shouldn't. Attach the tesla to your mount however you want, and then reroot to the mount.  
Moved to gameplay questions. 

Do not disturb the Kraken with your inquiries.   It has deemed you worthy, it is now moving onto another to bedevil.  Let it be.....
 
Glad you got it "fixed". 

Typically, when the question is asked "Why is my ship rotating or spinning?", you have set the trim.   Try nulling out your trim.  I'm not sure how to do this on console though.
 

Yes, for some reason it's thinking this is not a new vessel.    If it is a premade design (by you or anybody), change something on it, pull something off and put it back on, rename it, and launch.   If THAT doesn't fix the issue, then there's something wonky at work here.

I have seen reports that the frame rate in 1.7 is noticeably higher than in past versions. 

It's difficult to say, as we can't see your whole ship in the pic.    This 'error' is usually caused by the main control core/cockpit not be in control of the vessel.  Right click the cockpit or the probe core, and select control from here.   If your main control core/cockpit is rotated, the Navball will line up with the core/cockpit like you see here.  Keep changing your cores until you find a good one.   
If not, you might have to learn to fly sideways, or flip your monitor on it's side.    

Moving to Gameplay Questions
And this little gem should help you out:
 

Ok, this is kind of an XY problem, sorta. 
To answer your question directly...  You can add fuel tanks or batteries to the top of your rocket.  That will shift the COM upwards.  
But that's not the real problem.    The real problem is your are not asking the right question.    Center of thrust really doesn't play that big of an issue with a launcher, unless you have some really funky designs (if so, pics please). 
The right question is, How do I get my COM above the center of drag? (paraphrased)
So, you have two options.   You can shift your center of drag downwards, or your COM upwards. 
To shift your CoD (which isn't displayed in the game), you need to add draggy bits (Fins) to the bottom of the rocket, or make the upper stages more streamlined. 
To shift your CoM, you need to add mass higher up on the craft.   One method I use is to set my fuel flow priority so that the lower of the main tanks empty first, leaving the higher up ones still full.   
Another option is to add a fairing to your payload or upper stages.  Not only will this help stream line your upper stage (if built correctly), but it also adds mass, so it works by shifting both your CoD and CoM. 
Others are going to come along now and add their very valid two cents, including some links to good threads on this topic, and how I'm technically wrong in using CoD.

There is also the harpoon part from KAS which will harpoon the ground, and then use the winch to haul you in. 
But with a 6km radius, you should consider docking with the surface rather than landing.  Treat it like a big asteroid, then use the KAS ground anchor or harpoon to finish the sequence. 

Launcher has been broken for a number of years now.   Don't use it. 

Yup.  MechJeb is notorious for having conflicting controls activated.  When it goes wonky on you, check all your settings....
In this case, turn off the ascent guidance!!  As soon as you reach orbit, make sure that is disabled, not just the Q limiter.  
In fact, Limit Q is also found under utilities, and if you enable it under ascent guidance, it also is enabled under utilities.   Anything enabled in utilities will still function even if the ascent guidance is turned off.    Including things like throttle and acceleration limiters. 

Make your pairs of tanks in pairs, but use guides.  I'm exhausted, can't keep my eyes open, but I'll try to explain how I used to do something similar for 8x asparagus stages, that dropped off in pairs.
1)  Slap your 4x tanks on the core tank.  Get them aligned just like you want.   Now grab something like the non extending antenna, and place 4x of them, aligning them exactly to a point on the 4x tanks.  Place them so you can exactly line up the tanks later vertically. 
2) Remove the 4x tanks, add 2x tanks, lined up exactly as you just did, using the antenna's as guides.
3) Add anything you want on all 4x tanks to the tanks now.  Doing this now will guarantee symmetry for these items. 
4) Alt-click the 2x tanks, and place these new tanks in the correct spot 90' from the first two.  Again, using the guides for alignment.  With a little practice, you can get spot on with the vertical symmetry of the pairs of tanks.
5) Now you have 2 pairs of tanks, in 2x symmetry each, top aligned vertically across the ship.  As long as 2x symmetry is selected, any part you now add to one tank, will only be added it it's twin on the other side. 
Oh! And 6) Remove the alignment antennas. 
 
EDIT: In this case, alt clicking is a good habit to get into.   If you are building an asparagus booster, You should make one pair first, and then adjust all your staging as necessary.   Chutes (for stage recovery), sepatrons, main engines, launch clamps, etc, should be adjusted correctly now.  And then when alt-click for the next pair, all the staging setups will carry over to the next set.  The set's of staging icons will be nicely grouped together to make it easy to separate them into unique stages.  
 

One rather dumb looking plane I made used all heavies to land, but when I wanted to taxi back to the hangar, It lraised the front gear until it rested on a set of mediums, which would steer.   So I had a medium set way out on the tip of the nose, and a heavy set a bit behind it.  

We're gonna need pics for this one, I think.  Mod list, KSP version, logs, etc, too.  
But first off confirm all your mods are the right version for the KSP version you are playing. 
Does it still happen after rebooting KSP? 
Was the station rolling with the shuttle, as if they were still docked, or could you only roll each one individually?
 

All files should be found under where ever you installed KSP.  If you can open them in the game, then they're in there. 
Although, I might have completely missed what you are asking.  A screen shot of your ksp folder and sub folders would help.
If all you are seeing is a shortcut to the game, then you probably accidentally moved the entire folder somewhere else.  Check the shortcut's properties to see where it's target lies. 

Probably done this a few times, but back up 30-40 m or so, and try again.  Sometimes the coupling action needs to reset...
 

I'm assuming KOR means "Kerbin Orbital Rendezvous".  If not, ignore the rest of this post. 
Well, you need to specify two orbital altitudes.  One for the target, and one for the active ship.
For MOR, I like to keep my target at 50k, and launch to 30k.   I don't have a lot of need for 'complicated' orbital planning in munar orbit, I usually am just docking with a station or mothership, and that's the pattern I've fallen into. 
For KOR, it really depends on the target.  I have stations at 100k, 150k, and 375k in the current save, and while I usually directly launch to them, or at least close enough I can do a rendezvous, I know I can do a Hohmann transfer from a range of altitudes, based on the vessels needs. 
There are others here who are much better at orbital mechanics than I, and they should be along shortly to correct me, but IMO, there really isn't a generic optimum altitude for OR.  It all depends on what your mission requirements are.    If you have a target at 90k, then launching to 75k and trying to catch up may take a long time, where launching to 200k and letting the target catch up maybe better.   
The greater the difference in altitudes, the less time it takes for one vessel to "lap" the other, giving you more transfer opportunities.    But the greater the difference, the higher the relative velocities will be when you do get that rendezvous, and that may take more skill/time/fuel/etc than you are willing to.    So for any target of a given altitude, you can say I want to get a transfer and rendezvous within X orbits or Y hours, and from that you could figure out the optimum altitude for your vessel.    But, that will vary from target to target, so..... it depends.