Master Archery Paralysis perk lasts for just a few seconds but definitely long enough to make things easier on you...
It should stack in a sense with weapon paralysis enchantments as the weapon would fire off as well as the perk on separate chances thus giving you a heightened chance to paralyze your target...
There are no creatures that I've found that are immune to paralysis as I've managed to paralyze even dragons a couple of times but I wouldn't be surprised if Alduin is immune to it as it would make fighting him far easier than it already is (specifically an Ancient Dragon does alot more damage than Alduin)...
I can't tell you the best paralysis time to use on enchanted weapons as it's all personal preference and I don't use it on my main weapons and have only used it a few times... Just go by how often you are willing to deal with recharging the weapon...
Paralysis poison doesn't stack as I believe that it goes by their resistance to poison (I'm not completely sure on this one though)... Paralysis stacks by firing off each chance separately which gives you a chance for all of your forms of paralyze to hit on the same attack or none go hit at all... You get a heightened chance for it to hit with multiple things giving a chance of it but the chance itself doesn't stack... I.e. if you have a 15% with the master archery perk and say 10% with the enchantment that doesn't mean you have a 25% chance to paralyze, it simply means you have two separate chances at 15% and 10% that will have a chance for it to work thus giving you a heightened chance for the effect to take place but not enough that it would become overpowered...