VoidSquid

Looks like this bug which as per the patch notes has been fixed in 1.11.2
https://bugs.kerbalspaceprogram.com/issues/26961

You could use an engine with gimbaling, e.g. the Spark, or the Caravel from the RLA Reborn part mod pack.

In the main settings menu:

Looks like the same issue as here: 
 

As per the change log for 1.11.1, this bug
https://bugs.kerbalspaceprogram.com/issues/26872
has been resolved  
or hasn't it?

Known bug in KSP 1.11.0, should be fixed in 1.11.1
  
 

Interesting... firing up my 1.11.0 test installation gives me this:

 
EDIT: And the flags I see in your screenshot are not in the usual flags folder but here \GameData\Squad\Agencies , and they are in DDS format, not PNG. As if KSP is starting from a wrong directory / path, very odd....
What happens if you quit Steam, copy your whole KSP folder directly to the C:\ drive, open it there, and double click the KSP_x64.exe, not using the launcher?
EDIT2: You log file starts with:
Mono path[0] = 'D:/#Steam/steamapps/common/Kerbal Space Program/KSP_x64_Data/Managed'
Mono config path = 'D:/#Steam/steamapps/common/Kerbal Space Program/MonoBleedingEdge/etc'
while mine starts with
Mono path[0] = 'D:/Kerbal Space Program 1.10.1/KSP_x64_Data/Managed'
Mono config path = 'D:/Kerbal Space Program 1.10.1/MonoBleedingEdge/etc'
You see the difference, there is a # in your path. And I'd almost take a bet that this special character is the root of the issue. 
As I said earlier, try copying the whole KSP folder to another place, e.g. C:\KSP, and try playing from there.

Looks like this bug, I'd think:
https://bugs.kerbalspaceprogram.com/issues/27204

Corrupted save game then?
And while I can't find that post now, I actually do remember having seen a post recently about an annoying bug that happened after repeatedly switching the editor between SPH and VAB.

I suggest you remove all your mods, get yourself CKAN 
https://github.com/KSP-CKAN/CKAN/wiki
and install the mods you want to have that way.
 

The flag problem is a confirmed bug https://bugs.kerbalspaceprogram.com/issues/26872
About the ladder issue, I don't know, maybe other fellow Kerbonauts can add add something here.

Thought so:
FAILURE_IMAGE_NAME:  UnityPlayer.dll
As per my experience, I think this is caused by an incompatible mod, not the graphics driver. I recommend then:
 

Known issue, see here https://github.com/jrbudda/KerbalEngineer/issues/66

Known issue, see here https://github.com/jrbudda/KerbalEngineer/issues/66

Known issue, see here https://github.com/jrbudda/KerbalEngineer/issues/66

Well, yes, it's occasionally a bit buggy, in particular with time warp, I admit. That's why I'm using this mod here:
In general though: if you're more than 2.5 km away for any given vessel, physics, incl. EC, won't be calculated at all. Easy proof: Have a vessel with a negative EC rate. Switch to another vessel (or the KSC) being far away. Time warp some hours, switch back: the vessel will have exactly the EC it had when you switched away from it, i.e. EC won't be drained any more than the very moment you left it.

Never had that issue myself, but there are a few threads about this problem, e.g. here: 
 

No idea atm, sorry, but a suggestion: delete (or better rename) your settings.cfg, this should create a new default one, and you can see it that works.

As per this sheet
https://wiki.kerbalspaceprogram.com/wiki/Key_bindings
INSERT toggles the staging display (it does, just checked).
Maybe check your settings.cfg if you accidentally changed that to your staging key (or added it as a secondary key) ?

I'm still happy with my Win7, but if you feel to go for W10, go ahead  
Yes, they will, do not worry  
Just copy your old KSP folder to your new rig, and that should be it. Provided you have a working graphics card and a good driver for it.

Mun already has the new textures since 1.8., do you have adjusted your graphical settings? Mine are:

That's quite a mod list, I give you that  
Pretty sure there are a couple of mods you're using that are not compatible / updated yet to 1.9.0, e.g. TexturesUnlimited 1.5.9.24 is listed as compatible with 1.8.1, not 1.9.0. Same with TextureReplacer v4.1, ReStock 1.0.3, etc.
I suggest you check if all your mods are good for 1.9.0
Also, I did read a couple of times in the past that UI scalings not 100% often caused weird graphic anomalies.

Check if the Trajectories "Use cache"  setting is enabled, having this not enabled can cause massive lag.

...or having a pilot in the vessel.
You need a probe core for that, plus connection to Kerbin.
Or: have it controlled by a pilot from another vessel.
In general there are two different types of antennas, direct (e.g. the Communotron DTS-M1) and relay (e.g. RA-15 Relay Antenna), the latter ones can relay a signal, the former can not.
So, let's assume you have a vessel with just a Communotron 16 antenna in orbit of Duna. That antenna, even if you have the most powerful ground station at the KSC, is simply too weak for a direct communication. Now add a RA-100 Relay antenna in Duna orbit to that picture: the little Communotron 16 is powerful enough to connect to the close by RA-100 Relay antenna, which in turn is powerful enough to connect to the KSC: voila, you have communication, provided the Communotron 16 has line-of-sight to the RA-100, and the RA-100 has line-of-sight to the KSC  
Of course, this is just a simplified picture, but you get the idea behind direct antennas and relays.
I followed this guide here, works perfect, might even be a bit overkill:
https://wiki.kerbalspaceprogram.com/wiki/Tutorial:Setting_up_a_CommNet_system
 
Here's an excellent video explaining the whole CommNet concept, including how to remotely control another vessel with a pilot:
 
If you really want to dive into this topic, you can check out this post
 

I wouldn't go that far yet.
As per the error log, you have an "HP Pavilion 15 Notebook PC" with an Nvidia 840M. Many notebooks (including my own) have two graphic card chips nowadays, can you check the Nvidia one is enabled for KSP? Can you try the other, not-enabled chip (there should be a utility program allowing you to select which graphics chip would be used by what application)?
Quite possible the low-power-consumption standard chip is used and that that one can't do DX11 properly.