Yes, you may put your CGI programs whereever you like and the web server will pick up, and parse them as CGI if you put the appropriate extension on them.
You may also create a directory named cgi-bin and place them in there if that makes you feel happier.
Dreamhost use Analog v 4.x for analysing hit statistics. Hopefully this will be upgraded to version 5 soon (please?).
No problems with the MySQL server. I wasn't even aware that the service had problems in the first place. Seems solid to me.
After scouring the net for a few years and using an extensive number of hosting providers; I have yet to find one as friendly, flexible and helpful as dreamhost. If you really want to tweak things with your setup but can not afford to fork out for your own dedicated server, then I think you will find that Dreamhost really is a dream!