Keyboard And Computer Doing Random Things

I am not finding any malware in your logs. However:

In ADWCleaner, do you know what these are: (If not, remove them.)
PUP.Optional.Legacy, omaha
PUP.Optional.Legacy, omaham

After removing, right click start/run/ and type in %temp% and remove all that junk.

If you are still having issues with your mouse, I suggest you post in the software forum.

Since you are not having any malware problems, it is time to do our final steps:

1. We recommend you keep Malwarebytes Anti-Malware for scanning/removal of malware.
2. Re-enable your Disk Emulation software with Defogger if you had disabled it in step 4 of the READ & RUN ME.
3. Go to add/remove programs and uninstall HijackThis. If you don't see it or it will not uninstall, don't worry about it. Just move on to the next step.
4. If running Vista, Win 7 or Win 8 or 10, it is time to make sure you have re-enabled UAC by double clicking on the C:\MGtools\enableUAC.reg file and allowing it to be added to the registry.
5. Now go to the C:\MGtools folder and find the MGclean.bat file. Double click ( if running Vista, Win7, or Win 8 or 10 Right Click and Run As Administrator ) on this file to run this cleanup program that will remove files and folders related to MGtools and some other items from our cleaning procedures.
6. Any other miscellaneous tools we may have had you install or download can be uninstalled and deleted.
7. After doing the above, you should work thru the below link:
   • How to Protect yourself from malware!