(free account) Do you get analysis report for free if your opponent ran it for you?

Title.

If that's intended behaviour, are these unlimited?

No

I think you can. Sometimes it doesn’t work like that though. Chess.com’s api is strange

I had this happen at least twice to me today. I go to my game list and the game is analyzed. I didn't analyze it (and I've run out of reports for today). So probably opponents did it, right?

I know it's possible. My friend has a free account and sometimes he asks me to analyze his games so he can see the accuracy. Sometimes chess.com doesn't "remember" (for a lack of a better word) the analysis, though, but usually it does

Yes, if someone else runs the a review, it will show in your archive that it was run. I don't know if you get the full view or not if you try to visit it.