Thanks for reporting. To cover both of your points:
We've been able to replicate this when loading into a flight at a gate/parking in MSFS 2024 with State Saving enabled. We'll investigate a fix for this ahead of the next update to the PA38 Tomahawk.
We've logged this to look into further; however, I'm not sure if it will be possible for us to do anything about it, sadly. Our PA38, and other aircraft like the F28 and Vulcan, use clickspots to move the player to different camera positions that rely on the MSFS' core camera system. As Chaseplane overrules the default MSFS camera system, these camera positions don't exist with Chaseplane installed, so the camera doesn't move.
Mark - Just Flight