Is it normal for an elevated deck to sit on posts like this?

I built a second-story deck off my old house a few years back, so I can tell you what should be there. Every post needs its own footing, ussually a concrete pier poured below the frost line with a metal post base sitting on it. If those posts are just bolted or sitting flat on top of an existing patio slab, that's a red flag, because a slab that thin isn't designed to carry that kind of concentrated load. Sometimes they do dig through the slab and pour a proper pier underneath, so it's possable what you're seeing is fine. But you can't tell from eyeballing it, and neither can I.

The permit thing is actually the easiest part to check. When we bought our place the seller 'had permits' too, so I called the building department and they pulled the file in about ten minutes. Either there's a record with an inspection sign-off or there isn't, no middle ground. Also, dark paint on a deck that new is worth a second look. I repainted a 12x16 deck two summers ago and found soft spots the previous owner had painted right over. Paint hides checking and loose fasteners real well. Ask for the ledger flashing detail too, that's where second story decks usually fail first.

Those angled braces holding up a big second story deck, that's the old knee-brace way of doing it and it depends entirely on the connections. Back when I helped my uncle on decks in the 80s we'd bolt those things on and call it good, but a lot of them were bolted through nothing but end grain and that's what lets go. Look at where those braces meet the posts and the beams. Are they carriage bolts with real hardware or a couple of nails? And get up there and check the house side too. A deck that size live loaded with people is a whole diffrent animal than a ground level one. Engineer money is cheap compared to what's hanging over those doors.

We hired a structural engineer before buying our place and it cost a few hundred bucks, way cheaper than finding out after closing. Mine spent like two hours poking around, checked the ledger attachment and everythign, then wrote up a report we used to negotiate money off. The whole thing over the sliding doors is a good excuse too. If it's ever leaked down onto that glass or the framing around it, an engineer or a good home inspector should spot water staining. Honestly if the seller's confident it's all legit they won't mind you getting it checked.

The engineer reply is spot on, and yeah the knee brace thing is real. Our neighbor has one of those elevated decks on angled supports and a few winters ago one of the connections worked loose enough that you could see the whole corner sag when people walked out on it. Turned out the bolts had never been tightened after the wood shrank. The engineer who looked at ours also made the seller show the ledger flashing, wich is the spot where a lot of hidden rot hides, so ask for that too. Ten minutes on the phone with the building department costs nothing, do that first.