Yes, you can use any cylinder rated for 500 psi or above. What you have to consider is how much weight you will lift with that cylinder. A cylinder with 500 psi will lift about half as much as one with 1000 psi applied. Where you attach the cylinder to your lift arms and how long they are may limit your lift to only a few hundred pounds. How much do you want to lift? You have to put some thought into this and give us some specs if you expect our answers to be anything more than SWAGs.
Yes, you can "T" into the line where the hose goes to your current cylinder and run that line to another cylinder. You can use a single-acting cylinder or a double-acting cylinder, but one port will have to be left open on the double-acting cylinder for air to vent/escape out of its unused side. When you pull your lift lever, the cylinder with the least weight will operate first until it gets to it's retracted maximum and then the other cylinder will operate. If you secure your mowing deck in the up position, then it will not move and your rear lift cylinder will operate. When you want to mow, you can run your rear lift to the top and secure it. With it latched so it cannot move, your mower deck will lift. If you don't mind them both going up/down together, then you don't have to secure them. This is not an elegant solution, but its quick and dirty. Another way to accomplish this would be to install isolation valves in your lines going to the 3PH and deck lift. That would take a lot more plumbing and fittings.
You won't have to worry about hurting HST operation as long as you keep your HST fluid at maximum fill level.
If you want to do this, I strongly suggest you find somebody who has at least a basic understanding of hydraulics who can put hands-on your project. Personally, I think the design and build of your 3PH or sleeve linkage will be more complicated than the hydraulics.