To answer your question about grilling, thought I would provide you with this. I work for CFD and this is what we have been going by. I will double check with Fire Prevention on Monday, but am pretty sure you will be okay if you follow this....
Pursuant to the Ohio Fire Code, Section 308.3.1 ....
(A)308.3.1 Open flame cooking devices. Charcoal burners and other open flame coooking devices shall not be operated on Combustible Balconies or within 10 feet of combustible construction.
Exceptions (which apply to Parker Flats):
2. Where buildings, balconies, and decks are protected by an utomatic sprinkler system.
308.3.1.1 Liquefied petroleum gas fueld cooking devices (LP). LP gas burners having an LP gas container with a water capacity greater than 2.5 lbs shall NOT be located on combustible balconies or within 10 feet of combustible construction.
In the case of Parker Flatts, it is either type I or type II construction. Type 1 being fire resistive, type II being Non combustible. Structural members, ie: roof, beams, walls, and floors made of steal, concrete etc.