Yes, there's a box in the admin section, just follow the path I laid out for you to get to it.

And nope, you can use WinZip for free for as long as you like.
You could test it by installing a back-up board, but that would be a lot of work. Really, all you have to do is check the date and size of the file(s) and give the sql file(s) a once over and look at them to see if they look right. Compare your database size to the file size. I believe they should be the same. Also, backups work for some shared servers. They work for mine. To check, after you backup in Threads, check the restore section for the date/size information. If it displays that day's date and the right file sizes (>0) then it should be okay.