I’m looking at a flight that lands in TLV around 7 AM.
Can I assume that the shul in the airport would have a minyan for shachris?
If not, what time can I expect to be in Yerushalayim, as I would like to daven there?
There should be minyanim in the shul. (after customs turn left, one flight up.)
Very much depends on how much time it takes you to clear customs, and collect your luggage.
I've done opening of AC door to street in about 32 minutes, (front row, no luggage) which can possibly get you to JLM before 8.
I've also taken close to two hours... (bunch of kids, back of plane, delayed luggage...) which will result in you getting to JLM closer to 10...