It's simple undo your old brakes and simply bolt on th new ones.I wont have a clue how to fit those, to my bike, so you say no cable so how do they stop the bike. is it all done by oil or what ever
Hydraulic brakes on a bike work much the same way as on a car , except one has a lever to apply the brake force pressure instead of a foot pedal.
Hydraukic brakes with callipers come already primed with synthetic fliud ( don't buy ones that use DOT 4/5 brake fluid) .
Measure the the length of the old brake outer cable and buy hydraulic brakes of a similar length.
Hydraulic with synthetic fluid are pretty much maintenance free unless one has a a leak or messes about with them when they don't need to.
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P.S
In #1 imv one has left it a bit late to change the pads , I would have changed them over well before the conditon yours are in.
Always have spares in your kit/chest so one isn't caught out.
I 'm still using a supply of pads I bought 6 or 7 years ago from AliExp , I bought a job lot /bundle for £1 a pair .