Regular tomatoes have a hard time in pots, but grape tomatoes do well if they have a cage to climb. They're the anti-gardening crop, thriving best on neglect. Got a dead potted plant? Chop it into its own soil with a spade, squish a baby tomato into it, pour some water over it, leave it in the sun and ignore it, except to pour water on if you're watering your other pots. Keep firmly in mind that you don't care if anything grows there, weeds or the old roots or the seeds or anything, you're just keeping the good bugs in there from dying out completely. That's the magic spell. In fact, they might not grow until you forget you planted them, then suddenly they'll appear.
I've successfully grown tomatoes in a pot, granted it was a decent sized pot (5+ gallon). They took a massive quantity of water daily and creative trellising, but it worked out.
Now squash. Squash is my struggle, but this year appears to be doing better.
I've definitely had some strange rogue plants before and sometimes I'll leave them in if it won't hurt anything. But I'd rip that one out if I were you, you don't want the roots weaving their way into foundation cracks. Rip it out and seal the crack up!
I have a very stubborn tree that pops up on my back patio growing through about a quarter inch crack in the concrete. It's grown as big as maybe 7 or 8 feet before when I've gotten lazy about chopping it back down. If the apocalypse ever comes that tree is for sure taking over the house.