This message found in the Pet Training Results is not correct. It should be saying "Your pet has gained experience" since only Mega pets stop improving. While the stats on your pet should be maxed by Ancient (in my experience) that does not mean that the pet has not improved. The pet has not improved message is a bad message and it makes no sense after the pet stats are maxed it develops more abilities at Epic and Mega. Your pet has improved quite a bit after five tiers of pet training. Please change this mistaken perception.
It's completely correct, as if you do badly enough in a minigame, you'll get no experience or stats.
They mean when your stats are already full. Your experience still goes up, but the screen message says "has not improved." It doesn't matter how you score, if a stat is not improved, it says your pet has not improved.
This message found in the Pet Training Results is not correct. It should be saying "Your pet has gained experience" since only Mega pets stop improving. While the stats on your pet should be maxed by Ancient (in my experience) that does not mean that the pet has not improved. The pet has not improved message is a bad message and it makes no sense after the pet stats are maxed it develops more abilities at Epic and Mega. Your pet has improved quite a bit after five tiers of pet training. Please change this mistaken perception.
The message is directly related to the pet's individual statistics, not its overall level rating. The stats may all be maxed out and as such will not gain anything in training so therefore they aren't improved... but the total points toward level advancement do improve. And even Mega pets can improve. If you happen to get a "selfish" talent when you reach Mega level, it's not necessarily a bad thing. You can continue to train the pet... and in some cases it might be advisable to do so. If the selfish talent happens to increase the potential of a stat, strength for instance, training to build it up to max again could possibly raise the percentage of another talent that's directly affected by that stat. It might only give you one or two more percentage points but that could be a game changer. Example: Say your pet's strength is maxed out at 250 and when you finally train your pet to Mega it gets the ability of Hearty. This will raise the pet's strength potential by +25. If your pet already has the ability of Fire-Giver for instance, it gives a X% boost to fire damage. This is directly affected by the pet's strength so by training up the additional 25 strength you might add another percentage point or two to the Fire-Giver damage boost.