The first question is linked to the second, in the sense that the power of the laser will define the possible cutting depth and working speed.
According to the manufacturer, you can cut up to 10 mm with a 22W laser, but this really depends on the material.
Personally, I wouldn't recommend cutting 10mm with the 22W laser as this would result in a poor quality cut and additional smoke/fire risks, but having tried cutting 6mm MDF, the cut was particularly clean.

It's impossible to give you a precise answer, as this is a vast field with many possibilities.
It all depends on the nature (species) of the wood, whether it's solid wood, chipboard or plywood in different thicknesses (standard quality, aviation, marine, etc.), the different glues used to make multi-ply will make a big difference and often a lot of dirt is burnt.
I use a Falcon 2 Pro 22W, which is more than enough for me, because beyond 10 mm, I systematically cut and trim the parts on a CNC.
Be extremely careful and make sure you have a suitable filtration system and a mask with fine particles and activated carbon specifically for this work, as some wood structures contain carcinogenic glues when they are burnt, cut or sanded.
I hope I've helped a little.