We've had several reports about Opera GX - and even regular Opera - not staying pinned. One user thinks it is due to the latest Windows update (1904) ... all I can say for sure is I haven't seen it. Then again, I use the "All users" install rather than the single user install, and that may be a difference.
No idea about moving tabs between windows. Especially on different screens. Though remember this is a fairly early preview still.