Processor Name: AMD E-350 APU with Radeon(tm) HD Graphics
Processor Architecture: AMD64
Graphics Processor: AMD Radeon HD 6310 Graphics (512 MiB, not found)
Antiviruses: Microsoft Security Essentials
Games Installed: The Sims™ 3 (1.69.43.024017), The Sims™ 3 Seasons (16.0.136.019001), The Sims™ 3 Island Paradise (19.0.101.022001)
Custom Content: Yes (196 found)
[WARNING WRONG EXE] 16.12.2016 13:56:32 Message: Incorrect Executable - Expecting: ts3w.exe, Got: TS3.exe.
[WARNING WRONG EXE] 16.12.2016 16:18:13 Message: Incorrect Executable - Expecting: ts3w.exe, Got: TS3.exe.
[WARNING WRONG EXE] 16.12.2016 16:36:57 Message: Incorrect Executable - Expecting: ts3w.exe, Got: TS3.exe.

That's what the Crash Log Analyzer tells me has caused the crashing of Sims 3 recently. When it first appeared, I checked my mods - got rid of my newest ones, since the problem had just occured (also got rid of Nraas toilet stall woohoo place, cause it still happened, when it was downloaded) and I uninstalled, reinstalled Ambitions. (Cause CLA says the skuversion for Amibitions is missing... I already used repair via Origin)

Point blank, I have NO clue what they mean in terms of ts3w... Is there a difference? If so, what is it?
I checked my extensions and file names for Sims 3 and none of them have the w on it.

I have a suspicion that this might be - mostly - related to my Ambitions EP, which is digital.
As it is, I uninstalled Sims 3 and Origins completely and will see if this occurs with a re-install, but without my Ambitions this time.

If you have ambitions through Origin you have patch level 1.69. I remember seeing somewhere that someone had updated CLA for 1.69, but the version you seem to be using is only good through 1.67.

Edit: I found the new version for you. : http://www.modthesims.info/download.php?t=580022

Edit 2: ts3w was the file that you could track down to bypass the launcher before patch 1.69. But after they gave the launcher the shiny new upgrade to allow it to disable your EPs they also made sure that you would always have to use the thing.

I used the updated CLA version - the same issue happened.

So, where would that file be located? And why would this happen only after I got a digital EP version, when I have been on 1.69 for months?

It would be found in Program Files in Game/Bin, but it is my understanding that patch 1.69 removed it. (I'm still on 1.67.)

As for why it's happening, CLA would have complained about the exe being wrong any time after you updated to 1.69. The fact that your game starts with an exe that CLA wasn't expecting it to start with is probably not the source of the problem. It's just the first problem it spotted, and it's apparently not looking for anything more.

CLA doesn't work with 1.69 period. The game itself on Patch 1.69 uses a different executable than 1.67 and prior did. The new version linked to is still a work in progress, unless someone knows of a fresher beta; Zoxell was looking for testers but that was some time ago.

Patches 1.67 and below use ts3w.exe.
Patch 1.69 uses ts3.exe (without the "w").

It's not a matter of using a shortcut to start the game, it's the one that's actually running and CLA at least through the versions officially available through download channels here cannot cope with that one.