Are the HARP refi rates typically higher than normal rates?
No, HARP rates are not higher than normal rates. In fact the base rate will start the same for all products. I have seen the Big Banks charging higher by up to .75 as they are trying to capture their servicing portfolio opportunities. You should shop away from just the bank you send your payments too. HARP is...

I had a short sale that closed in october. Bought a house in october with cash. how soon can i get a loan on the new house?
Conventional lending will be 3 years as already mentioned. You can put a "private" sourced loan on anytime you want. Today there are many aunts, uncles, friends with money earning no return at the bank. If you have to free up some equity this can be an option. You may not get the premium rates but...