"I bumped into my teacher at the airport."
I think it's ok too. But we often write like this: 在机场，我遇到了我的老师。 Anyway, the proper answer looks better.
No, here 了 has to come after the verb (indicates a past action). You should put it at the end when it hints at a change of state
Hi ThieumL. Thanks for the info. I’m glad the Chinese language is far less stringent than you described. Native here.