Padishar

I can't try it right now but I suspect that they've either never worked correctly or they were disabled at some point because they made it very obvious that the game had extreme garbage thrash issues.

I really don't think it would.  If you are convinced of this then set up a completely stock install and create a vessel that suffers from it and post it in the stock support forum.
The game doesn't store rotations like that.  It uses quaternions and these do not suffer from the sort of issue you are imagining.

The most likely reason for that file to be missing is that it was removed in KSP 1.2 (the code it contains is now in Assembly-CSharp.dll).  You should simply remove the reference to KSPUtil.dll from your project and it should build fine.  If you still have problems then the "Plugin Development Help and Support" sub-forum would be the best place to get help...
http://forum.kerbalspaceprogram.com/index.php?/forum/29-plugin-development-help-and-support/

It looks like your GPU decided to reset itself for some reason and Unity got upset about this.  I guess the most likely causes would be either a bug in the drivers, an overheating problem or an actual hardware fault.  Can you run any other GPU intensive games without problems?

You might be able to add an inflatable heat shield (or more than one) to the top of the vessel to make that end draggier.

These two fairly recent threads (one in the "popular questions" section at the top of this forum) talk about what is probably the same issue (or closely related) and many variations on it have been reported over the years.  Most likely is that some mod is causing the issue but I don't believe it is always the same mod.  See the "How to get support" sticky thread (3rd one below) for details of troubleshooting techniques and, if you can't deduce the source of the problem yourself, details of what other information you will need to provide for others to attempt to diagnose it (logs, mod list, etc.).
 

This is probably the common issue caused by the presence of extra inactive (usually virtual) network adapters.  The usual culprit is Hamachi though other similar programs can also cause it and even some network adapter drivers can create extra virtual adapters that do the same.  If you have Hamachi installed then remove it and test.  Otherwise, check your network adapters in control panel and disable or remove any extra ones that you can't account for.  I believe it has also been known for a machine using wireless that also has a disconnected ethernet adapter to have the same problem.  If this is the case then disable the ethernet adapter, either in the network adapters list or in device manager.

Upload your output_log.txt file to a file sharing site and post a link as described in here:
Is this the first version of KSP you have run or did you previously run 1.0.5 or an earlier version.  If so, then make sure you aren't starting the game with the -force-opengl or -force-d3d11 switches.  In any case, the output_log.txt (and preferably a DxDiag report) should help to narrow down the cause.

Well, I think it was probably intended to be accurate but a flaw in how it is implemented means it actually displays the number of rendered frames per in-game second rather than per real second.  Basically it will bottom out at (1 / <max physics delta-time per frame>) fps, if the framerate is below this value then in-game time is stretched and the display just shows the limit.

Please read the sticky thread that tells you how to report bugs in a useful manner (and then follow the advice it contains).

Basically, your main problem is that you are running the 32bit version, not the 64bit version so the game is running out of address space with all the mods you have.
Either change the steam launch options to run the 64bit version (I thought this wasn't necessary anymore with the actual release version but...) or simply run the KSP_x64.exe directly from an explorer window (or set up your own shortcut).

Well, I would suggest searching through the save file for all instances of RESOURCE and seeing what is used.  This may take a while.  Then you can look in the ModuleManager.ConfigCache file in GameData for the RESOURCE_DEFINITION blocks installed by your mods to find out what is missing.

It is actually possible to play KSP on a machine that doesn't have any VRAM.  I used to play it on a 2.16GHz CoreDuo laptop with 3GB of RAM running 32 bit windows (so KSP is limited to 2GB of RAM) and a NVidia Quadro NVS 110M that used shared memory.  I had to reduce the texture quality (to reduce the memory usage) and tweak various other graphics settings to get a reasonable frame rate, it still wasn't very quick, but it does run.
I also regularly play it on machines using an integrated Intel HD3000 or HD4000 that again doesn't have dedicated VRAM.  When I replaced the above laptop with an i7-4770K I initially had no graphics card but the integrated Intel HD still had a G3DMark 13x higher than the laptop...
Your GeForce 9200 has a G3DMark quite a bit higher than my old laptop (83 vs 46, see http://www.videocardbenchmark.net/low_end_gpus.html) so I would expect it to work though it will run quite slowly...
Edit: Here is the dxdiag from my old laptop for comparison with yours.  It actually reports 121MB of dedicated video memory so it probably has 128MB of VRAM.
 

You've messed up the second link a bit but I managed to find it.
There are so many exceptions in your log that I'm not surprised you're getting nasty crashes.  They start during part loading when Procedural Parts gives an exception for several of its parts.  Then there's an exception from Scatterer while trying to destroy something though it looks like most other plugins are just being initialised about then.  Then there are a couple of null reference exceptions from KAC when going from the tracking station to the space center.  Then the same Scatterer exception happens again when switching from space center to flight followed by an argument exception from DeadlyReentry (calling a GUI function from OnStart).
There are a number of exceptions from MJFARExt because it can't load the FAR dll.  I assume this would be normal if you don't have FAR installed but you do appear to as FAR also gives an index out of range exception when trying to build its voxel stuff.  There are then ~28000 lines of "Transform error" followed by, what appears to be FAR, getting upset about stuff being NaN.  Then there are also lots of other exceptions from other mods and bits of stock code presumably because the earlier exceptions have prevented some stuff from being initialised correctly.
I can't see anything obviously wrong in the .sfs but, if I had to guess at the underlying cause, I would say that the installations of either or both of Procedural Parts and FAR are broken and this is causing exceptions during the initialisation of the flight scene that causes everything to break...
Edit: Also, the exception from Deadly Reentry could be causing something nasty so that should be reported to the author as it should be fairly simple to fix.

Firstly, please don't post large logs in spoiler tags, there are plenty of file upload sites that would be much better.  Second, yes, this crash has happened because the program has run out of virtual address space (4 gig limit for 32 bit process) and was unable to allocate memory.