Can you do mouth to mouth resuscitation on someone with asthma who stops breathing?

Yes. Yes, but allow for a long time for them to exhale.
Yes... If someone with asthma stops breathing, rescue breaths should be provided. Call 911 and the operators can teach you how to do it, if you are untrained. There are courses you can take to get this training, if interested.
Yes. Asthmatics have tight airways, and may need more effort to get air in and out of their lungs.