I was loosening the headers on my B18, and the nuts were so rusted that a couple of the bolts started backing out of the head!

Is there something I can put on them so when I tighten them they stay in?
I ended up using PB Blaster and the others are OK.

Also, one broke, do I need to drill and tap it insert another double sided bolt?
Not sure if that's what it's called, I'm just calling it that.

 

they're called studs, yes you should drill out the broken one and replace it. It can cause an exhaust leak. Its not the end of the world if you cant get it out, but it should be replaced. Remove the nuts from the studs before you reinstall them, clean them on a wire wheel, then locktite them in.....if all else fails just buy and install new ones