FWIW, TN55S is helpful when mentioning the S.
Don't forget to grease the Supersteer bearing and the front drive shaft slip joint. No idea on your experience, but I just added 2 remotes, replaced the lift arm pivot seals and torsion rod (there are more correct terms, but close enough). I see you have the remote to the loader. Nice. The starter is a royal pain to get to for replacement. I added a couple of small hydraulic leaks under the hood doing it; to be repaired eventually. The quick connects are the automatic release kind (poor term), a lot more money than the lower model versions (pull the collar back to release the connector). I think I have one left of the auto release type. Water gets into the back and they get a little corrosion in there (how often do you take the hoses off for the loader - every 5 years?). I also have the first year. You will find some things are no longer available, or are a pain to identify parts wise. The loader joystick and the rubber mats for example. The earliest of that year have a different joystick. About when the hood/headlights changed they made some cab changes, the mats are not supposed to fit. The next to useless interior light is too much money. Eventually I'll stick an led strip in it. I put a wood strip across the headliner because mine was sagging (~1' in front of your head). A lot of parts are common across the Fiat line if you look hard enough. FWIW. This was the last year NH tractors had Ford on them, would have said TN55S New Holland, with Ford in small letters. Newer graphics sets don't say Ford (yours may have been repainted, not stickers. Mine has a plastic toolbox over the drivers rear fender. And I have front fenders. It had the under mount exhaust, but I converted it to the stack that you have. My tail pipe fell off (mower ate it) and I didn't like the exhaust down in the dry grass anyhow.
I have the other loader (not self leveling). I don't know about your loader mounts, but they were redesigned around 2003-4. One of mine was cracked, the other side had a broken bolt and a stripped bolt (on the frame/lower end). I welded extensions on the mounting plates to go forward to the next set of holes, as well as a welder opened the broken holes and welded in grade 5 coupling nuts in the stripped holes. No problems since. Someone had put a 3/4" bolt in the bellhousing end of the broken bolt mount. Their is a very close fit, but too loose common 3/4" size. Fortunately it hadn't damaged the bellhousing. Just adding that word of caution.
Oddly enough, there are a few fractional bolts on this tractor. And of course, being a European tractor (USA is just as bad) you need every size of metric wrench that's made (the Japs cut that down very nicely). You get to use your 'extra' 11, 13, etc, wrenches. The a/c line clamps, and the through bolts for the valve stacks are fractional. I think another clamp use (maybe one of the hydraulic pumps - formerly a USA owned brand, but now Bosch). Just to know that there can be fractional sizes on it, rare as they may be.
It has been a good tractor for me. TN55-70 are all the same engine, just have the injector pump tuned for the horsepower rating. The TN75 has a turbo (still the same displacement, but obviously adjusted for the turbocharging). The standard TN55 transmission (at least for the NA market) is the 4x2. I think all the S models have the electric shift shuttle transmission (orange shifter), and other premium features. The TN55 (mechanically) major distinction is that it has a lighter duty front axle than the other models. The other models had a 12 or 16 speed option (I assume a 2,3,4 speed shuttle box). Europe had an option for a 32 speed. There's a fellow on here by the name of Rick (one more letter I think, RickB?) that has been a wealth of knowledge (dealer and/or mechanic) on these. I did have a problem with the clutch once. I figured out it was one of 2 or 3 switches/relay/position indicators (been a very long time). I was going to shotgun them, as an older piece of equipment replacing a couple of $25 parts wasn't going to hurt in the long run (maybe avoid a future failure). Turned out I needed software to re-enable to the clutch. I took it to my then local service dealer because I had no choice in the long run; I'd see them to re-enable the clutch anyhow, here you go, call me when you're done.
I need to replace one of the front roof height lights. Haven't spent any time on it, as I would like to upgrade to a brighter light. Or even a curved light bar. Something to do this summer. Even though the 90% use will be for snow removal.
I wonder why your loader hoses have the elbows on them? Seems clunky and unnecessary. Oh, reminds me, one of my loader valves is a 'float' version, the other is not. The users manual isn't clear on that feature. 'May' have a float valve. I finally determined it had that, had to learn to 'push through' the resistance on the joy stick. I thought my joystick was damaged (or the valve). It was just a crusty 'push'. Duh.