1. As stated earlier, RBG is a reputable seller... I've bought from them before and would do so again in the future.
2. It's actually the opposite of what Zeph said... a .580 grip on a .600 shaft will fill thicker, not thinner. However, if you buy from RBG, this won't be an issue for you anyways as if I remember correctly, they only have .600 grips anyways. This should be fine for you as nearly all clubs now have .600 shafts.
3. I know others have used air compressors to install other types of grips but whether or not solvent and tape was used or if it is necessary, I do not know.
4. You could always buy the grips from TGW... I saw them on their website a while back priced at $2.98 each... they also had the gun for $12.99 so if you need fewer than 13 for some reason you may want to consider going through them. As with RBG, they only have the .600 core (not listed, but I called when I was ordering mine).
I've had these grips on my clubs for about a month now and they still look brand new. The tackiness is good but not over the top like a Winn grip... also they say that they will keep their tackiness and not become hard and slick. I have the soft wraps (the red ones) and love the way that they feel. Also, the installation is seriously as easy as they make it out to be; once you have the old grips and tape stripped off you'll have the new ones put on in less than 20 minutes.
If you are looking at a midsize grip you may also consider buying a regular size building them up with tape if you didn't want the wrap style... you should easily be able to put them over 4 layers of tape... just make sure to use regular masking tape and not double sided tape.
Here is the link to the grips on TGW:
It looks as if they are out of the soft wraps as well as the installation gun but they still have the other four styles in stock.