the war dec drops off of you as soon as you leave the corp

remote repping someone with a limited engagement timer (i.e. shooting a wartarget) gets you a suspect timer. remote repping someone always gives you their timers (except LE) so if they had a weapons timer you get it as well

So remote repping someone prevents you from docking if they can't dock?

yes

To clarify, if we have 3 people, A B and C, with A and B shooting at each other, and C repping B, A's flags do not matter. C inherits B's flags as long as the repping continues. So if I rep someone who's shooting (and thus has a weapons timer) I gain the weapons timer as well and can't use gates or dock. If they deaggress, both of our weapons timers will tick down even if I continue repping and we will be able to dock and use gates at the same time.

Here's CCP's giant chart http://cdn1.eveonline.com/www/newssystem/media/63443/1/logo2_actions2flags.png

First: Does a character remain attack-able by war targets after they leave a corp, or are they immediately immune to attack if they had no aggression timer when leaving?.

Second: When it comes to remote assistance, I am curious what happens if someone remote reps a war target if they aren't involved in the war. I understand that it allows the other parties to attack the person who is using the remote assistance moduals, but does it engage the 60 second dock/jump timer?

Thanks for the assistance.