What should I worry about when buying a used Porsche?

Looks like a nice car. Your question depends a lot on how much of a budget you have for regular maintenance and servicing. On an older 944, which is a fairly maintenance-intensive car, you should plan on spending $150 per month, averaged out, to keep this car safe and reliable.

I'm not sure about all the claims made for the car, since totally rebuilding a 944 engine is at least a $10,000 proposition in itself.

Whoever is selling this is taking a monstrous beating financially, so that should tell you something.

If you don't have $1500--$1800 a year to spend, in addition to gas and insurance, then this car won't work out for you I don't think.

I'm always leery about buying older cars because they can be such a pain in the "you know what".
This seems like a decent buy, however, Porsche's can be expensive little beasts from insurance to replacement parts.
As the old saying goes..."I smell a rat !"
The seller clearly states that he's hasn't finished the restoration.
$5500 is a low price for a Porsche with a "completely overhauled" engine ! It's pretty expensive to do this, even for a common motor like a Chevy 350. The phrase "completely overhauled" and "rebuilt" are ALWAYS overused and ALWAYS appear in these kind of ads, yet - so very few sellers have enough proof that it was actually overhauled or rebuilt. Some sellers say this when the cars/trucks engine etc. had merely had a major repair, not an overhaul/rebuild.
The link at the bottom goes nowhere.
Too much emphasis by using CAPS for things like bluetooth and every nut and bolt. This is a hard-core sales pitch using carefully selected words to try to impress somebody that doesn't know better.

Regardless of the situation, $5500 is a LOT to pay for a nearly 30 year old car. It's a risk that few can afford to take.
There are many sporty cars that still have stick shift, take your pick. Mustang, Camaro, Firebird... this list could go on for quite a while.

That is a pretty good example of a well kept machine. You will still have things break and parts availability could be an issue. But there is a pretty good online presence of Porsche message boards where you can get help with stuff. If you are good at doing your own work it will be good. If you are going to send it to the shop for everything you will go broke.