Alshain

There is a spot where 6 biomes are in close proximity, I think that is likely the best bang for you buck, so to speak.

As low as possible.  The height of the tallest peak on the Mun is a bit more than 7km, and that's near the poles.
If you are inexperienced however, it is easier to land from a higher altitude, you have more time for corrections.  This of course costs more fuel.

Well in that case it does sound like a mod issue, the only real solution to solving that is to remove each non-essential mod one at a time (or a few at a time) till it stops.  If it still happens, you may have to remove any mod parts from the craft and keep going.  If you can, make your first test with no mods and all and start adding back mods instead, that will let you know if it is a stock issue or a mod issue to begin with.

Depenmd
The answer to these questions are irrelevant.  If you feel the need to ask them, the answer is "no", do not upgrade.  If you at all care about your existing stuff, do not upgrade to a test version (ever).  You can copy the entire folder elsewhere though and still try the test with a new save game or with a duplicate of your existing stuff.  The game is not tied to Steam's DRM or any other DRM so you can have as many copies as you like on your hard drive.
Answers
1. It should, theoretically
2. Yes.  Though some parts have changed size, like the Puff engine.
3. Yes. Assuming no mods.
 

Your large docking ports there are on backward.  I can't tell if the small ones are, it looks ok from the image but if that one is already decoupled it could have turned around.  So it's not docking because you are on the wrong side and it's decoupling from the hubmax because the proper side is 'docked' to the hubmax.  It has nothing specific to do with the hubmax, but improper use of the docking ports.
Other than that, I would say provide a craft file.  There is a chance that you attached the part to the dockable side and then rotated it as well.  You shouldn't do that if you did.  Hold the Mod key (Alt in windows) and make sure it attaches to the node the correct way, do not use the rotation tool to turn it around 180 degrees.

So, I'm assuming Hottest and Coolest are self explanatory.
Critical part is the most vulnerable part to structural failure.  This means, that part is currently the closest to being at risk.  Critical Thermal Percentage tells you just how close, at 100% it's a gonner.  Note: Just because a part shows up doesn't mean it's close to death.  Even on the launchpad the system picks a part to display, you have to compare to the percentage.  You can also compare it to the actual temperature which is displayed in current/maximum format.
Flux is the rate at which heat energy is transferred in specific methods.  Internal Flux is the generation of heat by a part (engines/drills). Convection Flux is heat energy spreading through the air molecules, this includes atmospheric heating during re-entry. Radiation Flux is the heat energy radiating out, this can be augmented with radiators.  There is also conductive flux, which is transferring from one part to another that it touches, however KER deals in craft, not parts, so this isn't available.  With Flux a positive number means you are gaining heat and a negative means you are losing heat.
So, with that in mind if your combined Flux (Internal + Radiation + Convection) is negative, your overall craft temperatures should decrease, positive and it will increase.  Flux values are a good way for determining just how much radiator you need to offset internal heat for things like drilling or long burns with a nuclear engine.  However this requires you launch the craft to see the values so unless you are planning to revert or are doing some HyperEdit testing, they may not be that useful to you.

Your speed is too fast, too low.  If you do a real gravity turn with a typical TWR, that won't likely happen.  MechJeb flies in a standard pattern, which assumes around 1.5 sea level TWR (which is typical).  If you have 2+ TWR, you are going to be going faster while lower in the atmosphere.  Of course with the new aero, you don't need MechJeb at all to have the rocket fly itself.  You can now do a real gravity turn with SAS off and sit back and watch without touching the controls.  It's a bit challenging to get it set up right and if your TWR isn't right it won't work at all.  But once you get it started, it's hands off.

I need more information than the video showed.  Specifically about the KOCS-1 satellite. Get us a picture of that, including it's targeting setup.  Since you are dealing with directional antennas, make sure you turn on the 'cone' option in the bottom left corner of the map screen and get a picture of that as well.
Since you directly targeted a satellite, it may be possible to still recover that new unit, I suspect KOCS-1 has a more generic targeting and isn't reaching the new unit.  If it KOCS-1 is targeting Kerbin, the new unit may not fall in the directional cone of KOCS-1. If that is the case, simply re-targeting that KOCS-1 at the new unit should bring it back to you. (Hopefully KOCS-1 has more than 1 line of communication to KSC).  Omni-directional antennas do not suffer from this problem because they have a 360 degree cone.  However their range suffers for it.

One other bit of information about cones to be aware of is that cones expand outward from the source and continue to get wider until they hit their range limit.  Higher directional antenna have more narrow cones, but higher range.  They are designed for use with the outer planets. For example, if you used a CommTech-1 in cone mode close to Kerbin, it would produce a very narrow cone which could miss your communication satellites until it traveled out as far enough that the cone widened around your satellite orbit..  Watch out for this pitfall.  This can be avoided by using direct targeting mode instead of cone mode (i.e. do not target a planet) however if that satellite should become obstructed, you could lose communications unless another just happened to be in your cone.  Ideally you want your probes to use cone mode so it can grab whatever satellite is visible, but you need an appropriately sized directional antenna.  It's a very elaborate system, but a lot of fun once you get the hang of it.

On another note, I highly recommend learning to use the flight computer in case you lose connection like that.  You can plan a maneuver and then execute it from the flight computer before you arrive and it will automatically perform the maneuver even if it loses connection (as long as you send the command before it loses connection).  That way if you lose connection you don't fall back in the atmosphere waiting on the connection to come back.

The video on the IR thread shows you an example.  The arm must be attached to one of the station modules when it is deployed.  Of course, that module can't be attached by the arm, but every module after that can.  HOWEVER, as  I said, you can not grab modules with docking ports, ever.  As I understand itm any part that is put in motion by the arm or any other IR part can not have a docking port on it (though the station itself can having docking ports).  You notice in the video the station does have docking ports, but none of the other vehicles used do, the escape pod, the spaceplane, the rover, the artificial gravity segment of the station, etc all use the IR connector things.  This means if you want to move station modules then you want to build your station without docking ports.  I notice in your picture above you are grabbing the station which has a docking port, that isn't a good idea.  It says it right there on the IR thread....

Do not attach docking ports directly (or indirectly) to IR parts. It will make your life miserable. You have been warned!
 

It's bugged.  The developer that did it said it would be fixed SoonTM