A:AnswerIt depends how much internal storage you're backing up. When getting a external drive to run time machine on, I would recommend at minimum doubling your internal storage.
A:AnswerYes. I use both Mac and PC and always format my drives to ExFAT which works seamlessly on both platforms. If you prioritize on Windows NTFS then you can use Paragon NTFS to allow Macs to read the disc in native format.
My understanding is with the new Mac OS High Sierra there is a new file format that may cause some compatibility issues so if you are using that OS make sure to pick a legacy format not the HTFS+ I think its called.