For all of my batches thus far, I've just washed my bottles in the dishwasher, given them an extra rinse after the washing cycle, and called it good. I make sure to use non-scented dish soap. The extra rinse is probably more for peace of mind, but it could also get rid of any dish soapy residue. This method has always worked for me, but if anybody thinks it's a bad idea, I'd like to hear their arguments...
I also do as you described with my priming sugar -- dissolve it into water, throw it in the fermenter, then rack on top of it. This has always resulted in an even mixture.
I wouldn't boil the priming sugar, though. Just get the water hot enough that it'll completely dissolve the sugar.