While it may be legal most HOA's prohibit it. Both from a safety standpoint and to prevent the BBQ fumes from invading other units.
I doubt it. As it is a fire ordinance you can contact the fire marshal and ask them.
If it is legal you still need the property owners permission. Neighbors may find your cooking fumes entering their units very objectionable.
check with both city ordinanaces as well as the condo lease agreement/hoa agreement.
Depends on what is written in the lease.