Guild Wars 2

1) If Player A applies regeneration boon on Player B, is it Player A’s or Player B’s Healing Power that affects the amount health is healed by?

According to Wiki:
Health Healed by Regen is
5 + (1.5625 * Level) + (0.125 * Healing Power) per second

Common sense tells us that it should be Player A’s Healing Power because Player A is the one Healing; but considering the amount of lazy programming from Anet, I am not sure.

2) And how does regen work if, Player A and Player B both applies a 2 second Regeneration boon on Player B?

1) Its the person using the skill that gets calculated, so in that case Player A’s healing power.

2) If they both apply 2 seconds of regeneration at the same time then player B will have regeneration for 4 seconds, for the first 2 seconds it will heal based on the highest person healing power then the last 2 seconds will be based off the other persons.

http://wiki.guildwars2.com/wiki/Effect_stacking for the stacking information, the example for the duration stacking is basically exactly what you where asking.