I think it is a lot clearer. Maybe soften the first line a little as it is a bit harsh. You could lead into the email with
Hi,
Hope you are having a good day. Regarding the dates which you asked me about (or something in your own words) I checked with corporate housing and I need to leave Wroclaw by Thursday, October 16th. (then I wouldn't mention seeing him as that may make him think about it and may think you have expectations, I would just say) I know you have your test on that day so I hope it goes really well.
Thank you for your email on the High Holidays. I've been reading a lot about Yom Kippur and thinking about things that I may have done that have hurt you. I wanted to say that, although I know this process is painful for both of us, I deeply regret causing you pain (then don't look for validation that you have got it right, state the correct appropriate saying) and wanted to say may you be inscribed and sealed for a great year.
On a lighter note, I'm just off to town with the X crew. I hope you are enjoying your evening (or something like that as a way to sign off). - ITH
