If I use free hosting and they have their AdSense running on my site, can I still put on my own ads as well?
If your question is about having ads of two different publishers then it is allowed. For an example check these DP pages itself -there are the ads from DP as well as the thread starters ad. But you must be careful, if the page does not comply to the guielines both the publishers may be at risk.
You can only use adsense ads on freehosting sites that don't use adsense (Try freewebs.com they're pretty good and they dont place ads on your page)
Use 110mb.com, you get great amounts of space and bandwidth for free hosting, plus there are no ads and it is easy to use.
I already have a site. They just added their AdSense though. All I'm asking is if it's okay to put my ads on my site while theirs is running as well.