We can't deny players the later pets because some players don't find the minigame challenging enough.
1. Yes you can. But if you should is another question. The pets are 100% optional and if you have 1 or more pets the rest are just different skins. I mean a jumpkin is different than a rabby, but in essence it's the same.
2. Pets could have multiple ways to be unlocked. Right now we have the pokemon model: A player has to fulfil a task of varying difficulty to obtain a certain pet/animal/monster. But even in pokemon you can "buy" pokemon at casinos, or do certain quest and get them as gifts (lapras in red and blue) or have ingame trainers who are willing to give them to you if a certain requirement is met.
This could be quite creative. Like, one pet can be bought at the farm for 100.000 which is astronomical right now, but in the end it will be achievable; and you get one pet from an old woman who searches for a new home as she is too old to take care anymore; one can be rescued from other monsters and that will follow you from then on.
I really like the taming minigame, but i don't think that it is a good idea that you have 10 pets and every time the same game. I would be satisfied with 5 pets with the DDR (DanceDanceRevolution) minigame where the hardest is on jumpkin difficulty or just a little harder, but the rest should be something different.
- one pet can be exchanged with the girl that collects the plushies. Her daddy got her this strange moving doll and she would rather like a real doll. (mini yeti, or rabby or something other fluffy)
- one pet can be cought by fishing? You hear a strange tale from the Haddock/Griddle/Shady Merchant (or all of them) about a monter in the lake.
- one pet can be bought for a horrendous price from the rich people on the roof at the cafe
- one from the old lady that is too weak to take care anymore
- one can be befriended/rescued in the past of the time-travel-town and it will follow you when you get back to the "now" because it remembers you (First it is too young but then it is old and wise (with a beard))
and so on