As for leaving the country?
I’m assuming land travel would be best, and probably through Mexico? I’m not sure if one can travel to Canada without a passport. With Mexico, you’d really only need one to get back into the US, not so much to travel there.
A. The problem with your car is, someone can easily track you. Especially if it is an abusive spouse, who has access. The car rental, not the best way either since they know exactly where you go. I believe public transportation or walking is the best.
I would buy the laptop in place A.
Then buy a hot spot in place B.
I would not use Starbucks or free wireless elsewhere since it is not truly private.