Training speeds

[Alex Webster]

You could have an 18yr at 30Q and an 18yr at 25Q at the same price. All that it means is that the 25Q has greater potential.
Whether he realizes that potential is totally dependent on the manager training, playing, use of boosters etc. during the players career.

So, is there an upper limit beyond which a player can't improve? Sorry for asking such newbie questions!

I really want to get one fast trainer in my squad (preferably a striker where I'm weak).

[DiZZee]

Players will improve in Quality / earn skills points until they retire at 34 max. the rate of earning skill points does decrease with age.
If a manager invests time and boosters in training a player, there is nothing stopping that player from having a Q level of over 150 in Level 2 or 3. Not sure how long and how many boosters required to go from Q 25 to Q 150.

Like I said before a fast trainer may not always be the best player in your team. I would advise to build a squad of players that give you ratings of 7, 8 and 9 almost every game. anything constantly below those , is a waste of skill points.