Yes, and yes. The only things you can't train in the park are the throws. You just can't throw him any. Exit area, reenter ask him, spar, exit enter. You can train all kicks and punches in a few hours. Throws you could max after the game is cleared in the collections fighting unlocked guys. Though as you know, no point for the 3rd one at all. You'll spar there like in Shenmue 2, it's as if you know nothing again. So just max what you love using.
Good info. Just gonna add some more to this:
Sparring with Jiamin is a great place to strengthen arm & leg moves early in the game.
Every 2 times you execute a move it'll increase in strength by a sliver. This is much less of a hassle than Shenmue 1 where it would take 10 reps to strengthen a move (20 reps if the move was Moderate-level). Also, if a move has multiple button presses in it (ex.Tornado Kick) you only have to do the first part of the move for it to be strengthened. Doing the additional inputs (ex. the second kick of the Tornado Kick) does not add to your count, so just do the first part.
One sparring session with Jiamin lasts
1 real-life minute (which is 10 in-game minutes).
Once sparring ends, if you immediately talk to Jiamin again he won't ask if you want to spar. To get him to ask you again you'll have to do one of two things:
The long way = exit the South Carmain Qr. (the closest exit is the Green Market Qr. to the northeast), re-enter it, and then speak to Jiamin again.
The quick way = after a sparring session save your game (standing near Jiamin), quit, and then re-load it. After you load the game you can immediately talk to Jiamin and he'll ask if you want to spar. This method saves you a lot of in-game minutes that you'd waste leaving and re-entering South Carmain Qr.
Other Stuff:
--The
Moves Scroll in Shenmue 2 is a lot less detailed. There's no white-color that will show you how much you've strengthened a move after a sparring session. Also the color of the strength bar doesn't change as a move reaches "Moderate" or "Advanced" level.
--I haven't maxed-out all of my moves yet but
I haven't noticed any of Ryo's moves changing in animation once they're at the Moderate level. That's a damn shame because that was one of the cooler things about Shenmue 1.
--You can strengthen
Throws by using them in Free Battles.
Each time you perform a throw it'll increase in strength by a few slivers. Again this is much, MUCH less of a hassle than it was in Shenmue 1. I was able to max-out Arm Break Fire really early in my game (my Shenmue 1 data carrying over + free battle w/Sam & Larry + free battle at Yan Tin Apartments = maxed out Arm Break Fire. I did about 27 reps in that last fight; you only have to do the Forward,Back,Back+Throw part of Arm Break Fire to strengthen it).
--Lastly, keep this in mind if you're taking a lot of time trying to strengthen Throws in a Free Battle:
if you fight for longer than 1 in-game hour (6 real-life minutes) Ryo's life will start to quickly deplete and once it empties he'll collapse and you'll lose the fight. So don't fight for too long.