There may be a difference between BrE and NAmE.  I use NAme so I treat "any" as singular.  Look at this for some insight:'http://writing.wisc.edu/Handbook/SubjectVerb.html

Thanks all (or both? :) ).

I found the answer; the link was especially helpful.

I would probably say "happen", because all the ways I can think of to fill in the reference to "these" are plural.

If any of these things happen, then we will be in trouble.

If any of these possibilities happen, then we will be happy.