Can my deck handle a hot tub?

Decks are supposed to be designed for a minimum of 50 lb/sq ft. A hot tub is probably more like 100 psf. I'd be worried about the fact that the joists aren't attached to the footings - it suggests there was no inspection, which means it was possibly not built to code.

I wouldn't risk it.

Not that deck.

Let's see a dimensioned drawing with details please.

Here are the code requirements for deck framing for 50 pfs. The top table shows how long the joists can be between supports; the second one shows the maximum distance between supports (footings). There are also requirements about how the framing is attached to the house (ledger board).

I'm guessing you'll need an entirely new (much beefier) deck to support a hot tub.

I'd like to see a dimensioned drawing of the existing conditions, but based on the pictures, I wouldn't worry about placing a hot tub on that deck. It's not a second story.

You have the opportunity to do a flush hot tub... do that!