Welcome to the forums.
I talked to my dealer about synthetic hydro in my tractor when it came up for service. He said he's had a couple customers that switched to synthetic and weren't happy with the switch. Seemed to make the hydro more noisy and less smooth. I think they even switched back to standard hydro. I am running synthetic engine oil in mine, but not synthetic hydro. My dealer did have to change the hydro type he put in mine at the 50 hr. The first oil he put in was too heavy for winter use up here, and was giving me problems. I'll ask him what he switched to in mine, but I've had no problems since, even running in the hot (90's) summer running my bush hog.
See if you can find out what hydro oil is in your tractor now, maybe a change to a different oil will help the issue as well?
There is an adjustment to the forward/reverse pedals, to keep them "centered". When your tractor is sitting in gear, on level ground, does it sit still, or does it creep forward or reverse? Perhaps your pedals just need a slight adjustment?
I would talk to your dealer about the issues you're having. There really shouldn't be any "jerky-ness" to your movement pedals. I'm going to assume your hydro level is correct, and you can see it in your sight glass when on level ground? It can be really hard to see through the glass, the oil is so light and clean. They do make a dye you can put in it to make it easier to see through the glass.
It did take me a few hrs run time to get used to the pedals on my tractor. They are quite touchy, both coming on, and coming off the pedal. I have to very slowly press the pedal down to get a smooth take off in 1st or 2nd range. Same with coming off the pedal, very slow and smooth, or it's like slamming on the brakes. The "pedal response" is instant.
3rd range on my hydro I only use when I transport or "road" my tractor to my neighbor's or a buddy's house a few miles away. I never use that range around my place, or to do any work on site. The gear range is just too tall for "work", just for running at road speed down the road. And yes, 3rd range definitely whines pretty good while I'm using it, but once I'm up to full road speed, on level ground, then the whine becomes very faint, almost completely drowned out by the engine.