Pretty much every time I have posted on the support forums, the initial reply has been to suggest I disable all other plugins and themes, without offering any other hint of an explanation.
In all cases, I have already tried that before posting; I would not be posting if I hadn’t. This just extends the turnaround of resolving an issue to the point of unacceptability, such that it is much quicker to resolve the issue by debugging the code myself.
I have posted my findings on the issues I have logged, and I hope you will consider them for bug fixes in future releases.
Problems relating to issue 1 above have been logged before, 2 years ago: https://www.ads-software.com/support/topic/plugin-events-manager-bug-insert-category-image-not-working-when-link-url-none
I would contend that this is not a WordPress issue per se, as there is no such issue inserting images into standard posts or pages, but perhaps an issue of compatibility between Events Manager and later versions of WordPress.
Regarding issue 2, I did use the standard WP export/import to move a DB, and this was not entirely successful, so I would largely accept that the problems were the fault of the tool. However, there is an option within Events Manager to allow custom fields, and the default is ‘off’, so I wonder if this could have played a part. I have since discovered UpdraftPlus which may be better at migrating entire databases should I need to in future.