If the reservoir is higher than the upper helm pump it may well be a gravity feed system. If it is lower, even by a small amount and has a pressure gauge then it is a pressurized system most likely Hynautic brand. Loosing air in the pressurized system can cause loss of steering. Oil leaking will also cause a loss of air pressure.
Regarding the hoses. The large hoses are the left - right pressure hoses. It's not a supply and return but a left - right shuttling back and forth as you steer. The small ones are the return lines. IF this is a Hynautic system.
1st determine by examining the reservoir if you have a Hynautic system. They produced two different styles of reservoirs. Both will be outwardly similar with the gold colored label and sight glasses. Both will have a pressure gauge. One will have the relief valve attached to the bottom of the reservoir as pictured in Keysdiseas's post. The other will have just fittings on the bottom, the relief valve will be elsewhere.
You are correct that there should be no air in the hydrauilic lines, helm pumps, ram and auto pilot pump. The only air in a Hynautic system should be in the reservoir. Oil should still show in the sight glasses.
It is important to know if you are dealing with a Hynautic system or not before getting too deep into the system. The bleeding protocol is a bit different.
Pictures would help in identifying your system.
Because your OP was about obtaining a rebuild kit I did some digging, I have a Hynautic system. Seems a good idea to be proactive in finding a kit. As of yet I have not found one. I did find that
Seatech Marine Products will rebuild Hynautic helm pumps for $350. A reasonble price. With Dometic pulling support for Hynautic it's unsure how long Seatech will be able to get parts. When I get back to the boat I'll see if I can find model #s and contact them to see if I can order a kit.
If you find a source for kits please share your info.