Sorry, my phone isn't letting me quote you... disclaimer: I am VERY new to chickens...thus the name

I'll try to answer your question to my limited knowledge though... if I'm wrong someone with more wisdom please correct me!
I thought the noise of the Sevin dusting bag sounded tramatising, but what do I know...I went with the dunking method because I had the ingredients on hand.
Q 1&2: I used 3 buckets about 3-4 gallons of warm water in each. 1st had about 3T. Dishwashing soap (I hear normal Dawn is safe but I had Sunlight so thats what I used), & 1/2c. Salt...2nd. Buckets had about 1/2c. White vinegar 3rd bucket just had water. Dunking went really quick once I got under both wings...the lice seemed to die immediately!
Q3: It's already in the 90's here so I didn't blow dry them just did it early enough that they'd completely dry by dark (I'd guess about 3 hours)
Q4: I've read that lice don't last when they're not on a host so cleaning the coop isn't as important as it is if you have a mite infestation...I have sand in my run, so I sprayed it with Windex multi surface with vinegar(this worked to kill maggots so I figured it'd be ok), then I raked the sand good and dusted it with DE. (I had previously tryed dusting with DE to get rid of lice and it didn't work super well...killed some thougg) The coop has a PDZ floor and I did the same as the sand in the run. I pulled out the roost, scraped all the poop off, sprayed it too and dusted it with the DE. The nesting boxes I threw away all the bedding and did the spray and DE.
Neem oil SNINKS horribly...I'm sure it would work...hope the chickens wouldn't mind
Hard wood ash should work to put in a tray inside the coop for them to bathe in, the harder the wood, the larger the lye content and when the lice or mites have excrement, the lye reacts with the moisture and fat to kill.
I personally dunked my chickens the 2nd time yesterday in a Permethrin soln hoping it'd keep the mosquitos away...I'll have to see though...none of mine are laying now so I don't have to toss any eggs.
Hope this is helpful a little! If nothing else I feel your angst!! VERY frustrating dealing with illness!!