Do PMs that leave go back to being house members? Seems like that would be kinda weird.
Yes.
> Does the house pick one of its own members for the job, or does the majority party get to pick anybody at all that they want to be PM?
Officially they can pick a member of either house of parliament. In practice picking a Lord would be extremely controversial and probably lead to some rapid constitutional reform.
> Do PMs that leave go back to being house members? Seems like that would be kinda weird.
They usually won't stand in the next election, and go off and do something else - either private business or charity, or one of the less direct parts of government (the house of lords, embassies or the like - traditionally Europe was another destination but I guess no longer). In theory they could stay on and work as foreign secretary or whatever for the person who replaced them (or return to the back benches) but yeah that would be weird.
Yep.
> Does the house pick one of its own members for the job, or does the majority party get to pick anybody at all that they want to be PM?
In most countries (the UK included) the majority party will pick one of their MPs. Australia once had a PM die in office (Harold Holt) and have a person in the Senate picked as the replacement, so the replacement ran in the byelection for the previous PM's seat.
> Do PMs that leave go back to being house members? Seems like that would be kinda weird.
Yeah, but they've also been house members the whole time they were PM, so it's not that wierd.