Hi James!
After reading your post, I've added punctuation capitalization, and a little editing, to yield what I think you were trying to convey... please correct me if I misinterpreted it anywhere;
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My 1650 has a new back rail and motor mounts. This is the cub for my collection
--->meaning, you have other tractors, but this is your only cub?
--I'm not sure what the 'back rail' refers to (somebody help me out here). I'm 'motor-mounts' refers to the "Iso-Mount" cone-and-cap bushings that go between the engine cradle and frame. If you have the Iso-Mounts too tight, you'll get a bit more vibration transmitted through to the frame...
The tractor runs great, but has vibration problems- will these parts fix it?
--->which parts- the rail and motor mounts, or something you saw posted on the forum? Bad motor mounts or broken frame members will cause all sorts of interesting things to happen. I'm not sure what type of vibrations you're experiencing... but problems in the driveline or engine mounts can either CAUSE vibration, or cause it to be much more noticeable...
After pulling the driveshaft does it have to be put back in any particular way? I know that Bolens uses a balancing-driveshaft that must be installed in a certain orientation. Does the cub do this?
--->No Cubs that I've worked on used any sort of 'balancing weights' on the driveline. All the engines used on Cub Cadets are internally-balanced, as are the transaxles, so a symmetrical, centrally-balanced shaft is all that's used. I don't think there's any way you can install the shaft 'wrong'. If you have the shaft out, roll it along the edge of a flat table, and see if it 'bounces' as it rolls- the telltale sign of a bent shaft... if it's bent, either straighten it (if you're really good) or replace it (if you're not!).
Regarding the rubber disk that hooks the driveshaft to the motor- the front disk is egg shaped and the back ones are round? I have ordered new ones...
--->Depending on which model/year, that could be correct. Earlier Cub hydros had a solid pin/slot type coupler at the engine, and an elastic disk ('rag-joint') at the hydro input-shaft. Later models (your 1650, for instance) had an oblong-shaped rag-joint on the engine coupler.
I changed the hydo fluid, and while doing so, I took a good look inside. Everthing looked clean no metal shavings...
---That's a very good sign!
It's a good little tractor- I'll be putting a 3-point hitch on it!
---Congratulations on joining the Cub ranks!
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Is my translation correct?