Your computer will be faster with Linux also.
That's great your sister knows about Ubuntu , she might like Mint Mate even more.

If she knows how to download and burn a ISO disk she can make a live cd for you.
You can use Synaptic or Software Manager to get additional programs from the Linux repositories.
browsers - Firefox, Opera, Chromium/chrome, Qupzilla
Email - Thunderbird and others
Games - so many to choose from
anything Windows has you can find very similar for free...
Facebook is a website so any browser will access it.
I think Mint worked with my old wifi chip, and Ubuntu also.
Perhaps my chip broke, as it worked for awhile with Ubuntu & Mint then started having problems , that was when I ended up getting another chip.. when I could get no connection with any Linux system..
So yours may be fine, you'll know if it can connect easily or not.. generally it can find wifi and connect with only needing to put in your password..if you have password required.