1) How do I prevent Bittrex from selling my altcoins automatically? I don't see the "auto-sell" option any more.
click on Lab ---> Auto Sell.
Check whether you have enabled the automatic sale of any of your altcoins.
2) How do I buy altcoins again on Bittrex in the new interface? I don't see a way.
I love the old interface but there are few problems regarding the new:
The tokens/dollar value does not appear.
It seems that all your problems are in dealing with the new interface, this video from YouTube will help you interact with the site again
https://www.youtube.com/watch?v=-y8rYJns9sg