abuki We apologize for the inconvenience. Regarding the first issue, after confirming that the issue could be reproduced with the project you provided, I tried to figure out how to reproduce it from scratch, but as you mentioned, I was unable to find a way to do so.
Regarding the second issue, it’s true that this only occurs in Unity and plays correctly in the Skeleton Viewer. Based on my tests, this appears to be caused by invalid curves. These invalid curves refer to the sections at the first and last frames: 
For the handles to have this combination, with one side horizontal and the other angled upwards, the Separate option must be enabled. However, this is not the case in the project you provided.
It is unclear how this state was achieved, but it cannot normally be done. In fact, I confirmed that when the angles of both handles are adjusted to be horizontal, the video plays back normally on Unity.
So, in conclusion, I think both should be considered as issues for the editor. I’ll create issue tickets.