An Instructive Moment

After a long game full of errors we reached the following position.  This is from the 2016 Sudbury Ch. Black to move...

It's a good thing I had a fair bit of time left on my clock, because it took me nearly 35 minutes to make a decision. 

Here's what I went for...

So... the question is this: 

Was Qf5, allowing the rook endgame, a good idea?  Obviously black is better, but is it drawn with best play?  I posted my suggestion for white, but maybe there's better?  

I would love to see some analysis/debate about this position.  I think it could be very instructive as positions like this (or the potential for these positions) arise so often!

I might try to post more detailed analysis in the comments, but honestly I'm not sure how to evaluate the position.