Crossfire reduces holofields

Sniper also reduces holofields, if you can find any AT weapon with sniper of course.

and dose teleporting set off over watch? and what about engaging in a air assault? (set it off?)

Does being assaulted/engaged remove overwatch status?

What does it cost an aircraft to jink AFTER it has run its mission? It looks like nothing, no disadvantage, just a free 4+ for everything.
Does jinking at least remove the aircraft's ability to provide AA cover from that point on?

AA is still considered shooting, right?

Fighters and fighter-bombers can choose to ‘jink’ when
they have to make a saving throw. Jinking represents the
pilot desperately swerving his plane to one side in order
to try and dodge the enemy attack. All of the aircraft in a
formation must jink, or none at all. Aircraft that jink
receive a 4+ saving throw instead of their normal armour
save but lose their attack if they have not already taken it
(they are concentrating on dodging enemy bullets). Place
a suitable marker on the aircraft as a reminder it can’t
shoot.

AA weapons are designed to fire defensively against an
attacking enemy aircraft, and may therefore shoot
immediately after an enemy aircraft formation makes an
approach move but before it makes its attack. This is
called a flak attack. Note that aircraft carrying out a
ground attack mission that are armed with AA weapons
may shoot at enemy interceptors that fall within the AA
weapon’s fire arc. Making a flak attack does not remove
overwatch status from a ground formation.
Flak attacks may not be carried out by units belonging to
a formation that is marching or broken. This aside, flak
attacks are a ‘free’ or bonus attack, and making a flak
attack does not stop the unit attacking again later in the
same turn. What’s more, a flak weapon can make any
number of flak attacks per turn against different aircraft
formations, as long as it does not attack the same aircraft
formation more than once in a turn.