This is generally a user forum, so as a user, I'll give this a shot:
1) CGI scripts. I don't do this, but my wild guess is that you can. I don't see it being much different than other scripts/apps that get run on an account. You get shell access with /usr/bin/make, but I'm not finding gmake, though I do see /user/bin/gcc. I can't find server specs (they used to be somewhat easy to find), but they're Intel-like (model name : AMD Opteron(tm) Processor 4310 EE). I thought they were running Debian.
2) You have access to /usr/sbin/sendmail which works pretty well for lightweight tasks. I believe it's throttled.
3) Cron is fully configurable, including running every 10 minutes, within reason.