Heh heh, I knew you'd like that thing! Glad it's treating you right so far.
Some answers:
1. I like to glue badges on rather than peen the pegs over in case needs to be removed. I use a gob of ShoeGoo on the peg from underneath smooshed into backside of frame. Reliable to hang on and remove with no trace if you ever need to. Same on all badges, it just works well and completely reversible like it was never there.
2. Yeah, I think it is the original speedo and the miles are probably right for the frame. Who knows the miles on the motor, that's not original it turns out as you know, it's way BETTER!
3. I'm pretty sure carb is a 20/20 but just pop the cover & filter off, and snap a pic so we can confirm. Pull all the jets & post up the numbers while you are in there so we can critique.
4. Get your fresh rubber on there, those old tire probably won't explode immediately, but who knows when you are out feeling your oats and wanna see just how fast she'll go!
5. Idle sound funny? Sorry, not my problem anymore, did you push the choke back in? Here's your chance to learn more, start here :
Mixture screw adjustment, got a good link?
6. Somebody close by w/ a legshield trim roller tool please speak up. I sent a proper aluminum replacement and I believe the tool will be needed soon.
7. Yeah, you could shop for a proper seat, but maybe lower priority. Anybody holding?
8. Welding that broken brace. Been there, done that, look here:
https://modernvespa.com/forum/post2367050#2367050
(hint: frozen hamburger)
Finally, if you are itching to start 'improving' things, start shopping for a modern box muffler and researching flow matching carb, airbox & and intake port as well as drilling the heart in your filter if not already done. Next up would be to choose a nice kit.... then ignition and ......