Ah my favourite topic
Nice answers from roseflyer but I'll join in and elaborate too...
Variable displacement pressure compensated in-line pumps are the norm, as most aircraft hydraulic systems are closed centre systems (Constant pressure, variable flow). Vane pumps and open centre systems (constant flow, variable pressure) like the sort you'd normally find in power steering or maybe garbage trucks are generally not used.
As a general rule if the hydraulic system is a 100% duty cycle system (i.e. switched on all the time in flight) then engine driven pumps and/or AC
motorpumps are used. If the system is temporary duty (i.e. switched on only for take-off and landing) then DC motorpumps can be used. DC motorpumps can be lighter but are usually brushed motors so they wear out, and can overheat, if used continuously. Fluid-cooled AC
motorpumps do the job where they're required to run continuously. Some aircraft (Boeing 767) have bleed-air driven pumps instead of electric.
Varies depending on the size of the aircraft and flight control architecture; if the aircraft is small, has powered flight controls but has manual reversion (i.e. not fly-by-wire) then two hydraulic systems might do the trick. (MD
-80, Citation X)
If the aircraft does not have powered flight controls and the system only powers landing gear/brakes/steering then one system might do. (Beech 1900, Learjet 45)
If however the aircraft is fly-by-wire, with no manual reversion, you need at least three hydraulic systems to cover your various failure modes. (Airbus A320, Bombardier CRJ)
Older, larger airframes such as L1011 & 747 justified 4 hydraulic systems but A380 only has two! A380 gets away with this because it has local back-up hydraulic powerpacks for critical flight controls.
Cavitation is not strictly related to cabin pressure... cavitation is induced by low suction pressure supply to the hydraulic pumps, it has to remain at least above atmospheric pressure - about 15psi (you want to push the fluid into the pump, not let it suck the fluid), but ideally around 50psi to stay healthy. If suction line pressure dips below atmospheric pressure and you induce cavitation, the collapsing micro-vacuum pockets can damage the pump.
Suction line pressure is addressed with reservoir pressure, and there are different types of reservoirs. Small powerpacks might have spring-loaded reservoirs, but otherwise they are air pressurised or 'bootstrap' self-pressurised reservoirs.
The cabin pressure association would only be because cabin pressure is maintained by the service air/ac system, which is pressurised with bleed air from the engines. Air pressurised reservoirs use the same bleed air, but have their own dedicated line. If you lost bleed air, in principle you also lose your reservoir pressure supply - but if the reservoir is sized properly, the pressure within the reservoir will be maintained by the existing trapped air until the fluid level drops, i.e. to cover fluid delta needed for unbalanced-volume actuators, like landing gear or spoilers maybe.
There are generally two categories used on transport category aircraft - phosphate esters and red oils.
The phosphate esters are the skydrols and hyjets - of which there are various versions. 500B, Type 4 and Type 5 - type 5 being the latest and greatest. Practically all the Airbuses, Boeings, Bombardiers, Embraers and Gulfstreams are skydrol.
The red oils are MIL-5606, 87257 and 83282, predominantly used on military aircraft but also smaller corporate aircraft. There are pros and cons to both types but I won't go into that here.
Chevron M2V is worth a mention too - this was the fluid specific to Concorde.
Yes - accumulators are like hydraulic springs, they can be used to absorb transient flow peaks/pressure spikes or compensate for flow shortfalls. There are various types - air pressurised rubber bladders, pistons or metal bellows.
You might use an accumulator to help something deploy very rapidly, like spoilers or thrust reversers, or you might use it to hold continuous pressure on a parking brake for instance, but brakes and steering accumulators are very common.
Engine driven pumps are usually in the nacelle, and reservoirs/motorpumps/PTUs/filters are often clustered together in the wheel well on something like an A320/737, but will be nestled somewhere in the 'hell hole' tailcone area between the engines on a rear engined aircraft.
Some good resources;
Smartcockpit has hydraulic system descriptions for many aircraft too.
Feel free to PM
me if you want to know more specifics