Your first issue sounds like it is the same as another issue, that the "transpose" function isn't really what a musician typically considers transpose, i.e. it doesn't change the pitch of the note you're playing (so you could press the same keys and simply get the same sound as before but at a different pitch), it instead changes what MIDI Note events are sent to the sound generating engine. In many cases, the audible result is the same, but not always (a common issue being that split points change, which makes the front panel transpose function pretty useless if you have precisely designed splits and need to transpose to a different key to accommodate a singer, for example). The solution, as you have found, is to use the Note Shift parameter instead, which actually does do what you would more typically think of as transpose, .i.e. let you play what you would normally play and simply hear it in a different key. But it's an awkward solution, since it's more time consuming (especially if you have splits and have to do it for multiple parts), and also if you need to change Performances mid-song, well, you basically can't, because your transpositions (note shifts in yamaha parlance) disappear. If you repeatedly do a song in an altered key, of course, you can set up custom recallable performances for this purpose. But if you need to do it on the fly (e.g. singer is having a bad night and asks you to drop the key, or a guest singer comes up), well, you're kind of stuck.

It would be great if Yamaha provided a user option that would allow the front panel Transpose buttons to instead function as Note Shifts for all Parts. Or maybe it could be done by leaving those buttons as they are, but adding some new on-screen "key change" buttons (say, to the Live Set pages) that would provide this same shortcut. Just some better way to handle this, because it's a really useful functionality that we don't have in the Yamaha world.

Transpose does not move anything in terms of programmed values. What it does is pretends like you hit a different physical key. It just remaps your physical "C" natural key to a different key (higher or lower). That's it. Splits stay where they are at. The keyboard does not ever see the physical key (when transposed) you press, it only sees the transposed key. So splits and microtuning and anything else that uses specific notes will see the transposed note and will function differently when transposed.

In order for microtuning to follow a transposed instrument - you need to transpose the microtuning to match. Or, as suggested - use note shift. Transpose remaps keys (input-side shift). Note shift remaps pitches (output side shift).

AWM portamento has been a long-standing complaint. It's just the way Yamaha's tone generator works vs. some of the others. Here's a discussion that has a link back to the complaint on older generation keyboards - and other comments about Montage which is related to MODX - https://www.yamahasynth.com/ask-a-question/legato-single-voice

If you have a related microtune for different key centers - and it is valid to use the same intervals for each note - but start on a different pitch - then you could save multiple Performances with different note shift (and even fine tuning shifting if you want the other notes to be an exact pitch) and save these "key center" Performances. This way you do not have to consume more than one user micro-tuning slot. You could even add transpose, if you wanted, so the notes you play on the keyboard "match" the pitches coming out of the instrument. Unfortunately, transpose is not saved with the Performance so this would mean manually pressing buttons if this was desired.