How to read ebooks on Windows?

I was thinking of getting a Kindle for my mother, since we are moving to a place without many English books. Then I realized about the whole thing about Amazon's store being limited with formats and I'd be stuck using Amazon only.
I think the Nook app seems to be more accepting of different formats. They made an app for Windows 8 and 10 which is great.
Now I'm wondering a bunch of things:
Does the Nook app sync between Windows and Android?
If I get an ebook on the Nook app, can I use it on other apps as well?
Are there ebook readers with a built-in light under $100 that support this?
And lastly, how do I download ebooks outside of the Nook app if the answer to question 1 was no?

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