Adobe Bridge may not automatically stack sequences, but it can be used to create stacks and then carry out operations on those stacks. I'm assuming (untested) that this includes moving them to new directories.
Adobe Bridge is free, and a lot faster than Lightroom when viewing thumbnails. You don't need to import images, it simply operates on the ...
No, T3i firmware will not install on your T5. Firmware is always very specific to each camera model.
Magic Lantern is a free 3rd party firmware add-on that is available for many different Canon DSLRs. It unlocks many hidden features, but it is not yet fully developed for the T5/1200D.
You're looking for a concept called 'super-res'. There's tools in python to do it, but most is all one-off and custom due to the amount of tuning needed.
Some cameras are main-streaming it though, so you may see more tools coming out.
You can also look at some astronomical processing software, but you'll have to provide the decoded individual frames. In ...