sallehsi: before we go further in, you need to understand the difference between a proprietary system and non proprietary system
Canon, Nikon and Sony ORIGINAL Wireless flash system are proprietary system, they only works with their own designated signal. nikon will market their system as CLS.
anyway, for 3rd party flashes, mostly like a studio strobe, are just simply plain IR/optic trigger, they see flash pulse, they fires. even a compact camera can set it off.
another 3rd party system is using their own 'Radio frequency signal' aka RF triggers.
as for Yongnou 560 III, its just a plain flash that has built in rf transreceiver, provided u have the right transmitter(eg: rf603) to trigger them. so basically its a RF wl flash
i. you solve your first question with the YN flash...
ii. No, the HSS will not work with your A6000. because the transmitter you getting doesnt understand the signal from your A6000(nor it have proper connector to link to the hotshoe.)
iii. sony is famous for their swivel head. rotatable is boring

(check out sony cobra design)
if, if, you still have your old nikon sb800, use it. grab a cheap YN trigger for nikon, you will able to fire/trigger them without problem. just no HSS no TTL