I am using a Hifi Walker H2. It is a reasonable price, has bluetooth and no capacitive touch inputs. The UI is not great but the device is physically solid and works for me.

I pre-ordered a Tangara on their crowd funding. I am hopeful about the opensource hardware and software. Only reservation is capacitive touch scroll wheel.

Hrmm, based on the amount of corrosion on the hardware my bet is your barrel adjuster is probably frozen. Additionally the cable routing to the anchor assembly seems off. Start with penetrating oil on the threads of the barrel adjuster. You might need some pliers for extra leverage to free up the barrel adjuster.

Also with that much corrosion I would unseat the shift housing along the cable to check for corrosion (which will create resistance) and at least lubricate them with some light silicon oil (chain lube will work)

In the highest gear check for excess cable slack. Correct your cable routing (should be straight through under the plate, look for a groove as a guide) and if there is slack pull out the excess while the pinch bolt is loose.

Then start the process of indexing the gears.

Replacing the derailleur would be an option depending on how stuck the barrel adjuster is but chances are good for breaking it free (drilling, retaping and replacing the adjuster is probably too much effort for that model derailleur). If indexing keeps being a problem check the housing and cables for corrosion, consider replacements. They are cheap and will make shifting much smoother.

nope, the cable pull ratio is mis-matched. the shifter is 10 speed mountain series so expects a 1.2 pull ratio derailleur. all shimano 9 speed rear derailleurs use a 1.7 pull ratio. see https://bike.bikegremlin.com/1278/bicycle-rear-derailleur-compatibility/#1

you will need a shimano dyna-sys 10 speed rear derailleur for that shift lever

Post mount brake pads would generally be the description.

When replacing this type I generally use some Jagwire Basics cause I am cheap. On other rim brake types I have used KS Salmon pads and they do help performance, especially in wet conditions. KS site has models listed by mount type see https://koolstop.com/collections/internal-backbone-smooth-post-cantilever

Current chainline +2.5mm: (118-113)/2 (assuming both spindles are symmetrical)

Based on experience above 5mm chainline difference is when shifting suffers

Length doesn’t damage tapers. Mismatched taper types will, all of this sounds like JIS tapers. ISO tapers not common so just check the specs on the new spindle, shimano uses JIS so folks trying to be compatible will follow suit.

Smaller round chain rings, pretty sure the oval 48T will work. I would measure the front/back chainlines and make a judgement call.

Short answer, yes.

Excess cable length would be hanging past the derailleur pinch bolt. It sounds like you are talking about making the housing shorter. Specifically the housing closest to the shifter. Doing this will involve loosening the pinch bolt and pulling the cable all the way back to the shifter. Once the housing is chopped the process is going to be the same as installing a new shift cable. In fact using a new cable may be a good option. Once the cable is routed back to the derailleur and pinched, indexing the gears will be the last step.