Beyerdynamic DT 770 PRO with xbox one compatibility

if you connect up to the controller (like you would earbuds) then yes, its not a hard setup to use equipment your'e talking about.

the xbox branded adapter is likely overpriced. it should be a standard 4pole 3.5mm headset jack. you will need an adapter yes (to split from the 4pole 3.5mm to two separate 3pole 3.5mm jacks for mic and headphone). these are often called headset adapter cables, pc headset to console adapters or various other names and are often fairly cheap (can be $2-5 at cheapest for low quality ones)

controller->splitter->amp->headphones. if you use a microphone (such as modmic) you will go direct to the mic side of the splitter (no amplifier).

check out amplifiers from fiio. the a3, e09k, e11, e10k, e17, e12 would all work. if you're spending more than $100 then the schiit magni is worth looking at as well. the fiios will give them a warmer sound and cut the harsh edge off the treble. the schiit will be fairly neutral and maintain the bright treble and not give a warm overtone to everything. depends on what kind of sound signature you want.

as far as adapter cables are concerned, brand doesnt matter just function.

no, as far as if you want/need the block with buttons which attaches to the controller... thats up to you (would add a mute button) but its not necessary unless you want a mute button (unplugging the mic would work too).

4pin, 4pole, trrs(tip-ring-ring-sleeve). its known by a few names



basically 4 separate parts on the connector. 3pole (trs) only has 3 parts on the connector.