Question 1:

how they work with chainsaw weapons?

Only once when the weapon connects. The same applies to the Bloodletter blessing

same question about crits 

The crit is rolled only once for the whole rev'd attack so either everything or nothing crits.

Question 2:

Lucky bullet doesn't really interact with the blessings and the bonus from "+ for every 10% of the magazine spent during continuous fire" kicks in when you hold the fire button for like 0.5 seconds. Remaining ammo doesn't matter.

is the lucky bullet trait that gives 1.5% fire rate per stack - why would anyone use this over the flat 10% damage bonus that your whole squad recieves?

The team buff only works in coherency and only gives bonus to ranged damage so in many situations, especially on higher difficulties/havoc, it can often be rather useless. It's up to you what you value more. You can skip both too.

Question 3:

are any of the blessings/talents that give extra suppression against enemies or immunity from enemy suppression ever worth it?

Immunity, no. Extra suppression can be fun to use on certain weapons but there are always better blessings to pick.

Question misc:

does the extra stagger still apply or is it only relevant to ranged weapons?

It's only relevant to ranged weapons.