I haven't lived in an apartment since 1979, but that seems really "out there".
$250 application fee? No way I'd pay that!
$350 deposit per pet is reasonable - they can do a lot of damage if the owner is sloppy. Most places don't allow pets at all for that reason.
If he has to buy insurance from "their" insurance company that smells like a kickback going on. I'd tell them "NO!" Besides, why do the require renter's insurance at all? If the guy wants to assume that risk himself that's his business.
$150 for trash put out early? What about people who work shift work like I did? Sometimes I'd leave at 5:00 PM and not get home until 9:00 the next morning. Forget that!
The income/credit requirements are reasonable. What landlord wants to deal with deadbeats?
No barbecue grills is reasonable - the fire hazard is obvious. More than one apartment building has burned down because of some idiot kicking over a grill of hot coals.