Hey Riszard : )
1a) My preferred method is dry erase marker on clear plastic or as you mentioned, pencil on paper.
No mech unit on Mission 1. Mission 2 there is a mech unit (truck) on B6
1b) you may distribute damage points as you see fit between commandos.
2) Any commando can fulfill missions 1 and 2. You have to use a commando special ability (CSA) ACTION at the required location to fulfill mission. (this only means that the commando is using one of his actions to perform the mission goal - not that he is using his innate ability. )
3) Correct
4) Flip counter, mark up the spot with an X, or use dice, piece of paper etc : )
Thank you for your questions! Will wait a few more days until I update file.
Hope this helps.