Jas0n

I would check your staging. If you have the engine and the decoupler in the same stage, mechjeb thinks you're ejecting the engine right as it is being fired.

You have five different versions of Module manager. While this in and of itself is not a problem because only the latest version will load, it shows that some of the mods you tried to install are outdated. 
I recommend going through all the mods you have installed and make sure they are all compatible with KSP 1.3.1.

You did follow all the instructions located here right?
If you did then I would post in the thread, where people are likely to be more experienced with this specific mod.
 

It's a visual glitch caused by scatterer. As you have found out, launching a vehicle fixes it.

mono.dll errors tend to be caused by incompatible mods.
You have a large amount of mods installed. I would check to make sure that each one is compatible with KSP v1.3.1. Keep in mind that mods in KSP are not forwards/backwards compatible, so a mod that is compatible with 1.3.0 isn't necessarily compatible with 1.3.1. 
A good way to find out if each mod is compatible is to go the forum thread for the mod. Or you can pinpoint which mod is causing the crashing by removing half of your mods and testing. If it crashes, you know the troublemaker isn't in the half you removed, and vice versa.

It is a purely visual glitch caused by scatterer.

It's probably some that has to with contracts, maybe try deleting play your way and see if it runs smoother?

That's a stock feature. It's accessed through alt f12 on windows. The video shows an older version of it, in the current one the infinite fuel and stuff is found under cheats.

your Module manager is out of date, assuming you are using KSP 1.3.0. 
Make sure you get the BDarmory from here https://github.com/PapaJoesSoup/BDArmory/releases
And its dependencies: https://github.com/jrodrigv/PhysicsRangeExtender/releases

That sounds more like a problem with the copying and pasting of files than a problem with KSP itself.

It's because you have FAR installed. It has always done this for as long as I can remember. I presume because FAR calculates aerodynamics based on voxels and would require an impractical amount of calculations for updating it before the part was placed down.

Logs? Mod list? I'm guessing that you modded ksp and broke it.

You can find your version in the readme file. And if you had mods installed and it updated the mods probably broke.

Are you sure that you put the mods in the right folder? Also, what directory is your KSP game in? If it's in programfiles or some other system directory it will have problems loading mods.