First, welcome to the forum!
Interesting question. I'll quote the spells for reference:
It would really depend on the DM since 5E is all about "rulings" instead of rules.
I would not allow it since the Simulacrum is part creature/part illusion. While Simulacrum does say
"otherwise be affected as a normal creature," it is not a creature, which is the requirement for True Polymorph. Additionally, since the Simulacrum is ice/snow, it is partially an object, but obviously a
magical object, so True Polymorph would not work in that way, either.
Now, if a DM did rule it was possible, as a player I wouldn't dispute it either. So, I'll respond as if it was ruled to be possible:
Correct. Simulacrum states
"Otherwise, the illusion uses all the statistics of the creature it duplicates."
No, it would not be an archmage. It would be a 19th level bard--assuming you used the
wish to make a Simulacrum of yourself.
Again, I would rule "No" because even with True Polymorph allowed, it states
"It retains its alignment and personality." Simulacrum's cannot learn or advance or replenish spells, so it still wouldn't be able to IMO.
This is more along the lines of using True Polymorph to change an object into a creature. Once permanent,
"you no longer control the creature. It might remain friendly to you, depending on how you have treated it."
Whether or not you could then do it again would depend on how the DM has it react.
It's an interesting concept...