[[Q:] Does Production Capacity affect all simultaneous productions?]

Worth noting is also that unless you have two assembly blocks there will be only one production line. So, one big block of say Xanion wont give you two  production lines. Two blocks of Xanion will though, and so on. I didnt realize this until yesterday when I rebuilt a carrier and replaced several smaller production blocks with one big.

[Out of sector activity stops]

For me I can start a ship mining while in the same sector, it will happily mine as long as I stay in sector. When I  switch sectors it finishes its roid and then goes to sleep. Remote orders do nothing. When I switch back it sometimes restarts mining, sometimes just sits there.  This is on the 0.21.4 production version.  Love the game :)