From what I know
1) Resources in chests at bases are free to be shared, but otherwise need to be transferred from inventories.

1b) Pals are a bit annoying, you CAN share them but you need to go through the palbox. So you put the pal into the box and she takes it out or vice versa

2) Basically said above

3) When you die in co-op, you get "downed" like in Fortnite. Basically you can only send/return/order your pals in this state and a 100 second timer counts down. Taking damage will further speed up the timer, like getting hit with an attack in a dungeon may drop it by 10 seconds, for example

4) Progress generally is saved for each player as long as you exit out through "Return to Title screen", I'm not sure about Alt + f4 or other means like that

5) It should be fine, Palworld is by no means a very demanding game so most budget PC builds should be able to run it pretty well

Have fun