This note seems to indicate suing out of state corporations in state courts is often accepted, and the exceptions seem to be cases where there's no real connection for the corporation to the state: https://www.law.cornell.edu/constitution-conan/amendment-14/...

I also saw https://en.wikipedia.org/wiki/BNSF_Railway_Co._v._Tyrrell where the company does have some presence in the state, but it was not its state of incorporation or principle place of business, and the plantiffs were not resident in the state and the events in the case didn't take place in that state either.

On enforcing the judgement, I would assume under a Writ of Execution local sheriffs could seize Facebook property at their offices in Austin or Dallas, or their data centers in Fort Worth. Those buildings (if owned and not leased) and/or their contents are certainly subject to judgements in the state of Texas.