What kinds of Torah jobs might an American yeshiva man find in Israel, and where?
Something paid, but it doesn't have to be a lot. Something that doesn't require Hebrew fluency.
Does this exist?
They totally exist, but you need to get into the yeshivas as a tutor at minimal pay, and then when something opens up/they need a tutor you already have an "in"
There are lots and lots of kollel men who want to be a rebbi/maggid shuir/shoel umeshiv ect in an american yeshiva or kiruv program and there are not that many positions.
They are also not high paying at all.
If someone is good at fundraising and is coming with experience, and has a niche that they have identified they can open a yeshiva.
