If Ambitious Augmenter has -1/-1 counters on it when it dies, that ability will include those as well. This may result in the Fractal token dying.

If enough -1/-1 counters are put on Ambitious Augmenter at the same time to make its toughness 0 or less, its second ability will see all of the +1/+1 counters it had when it died as well as the -1/-1 counters it had, and an equal number of each of those types of counters (plus any other applicable counters) will be put onto the Fractal token.

When comparing the mana spent to the creature's stats as the increment ability resolves, it's possible that the stat that is less than the mana spent changes from power to toughness or vice versa. For example, say you control a 1/3 creature with increment and you pay two mana to cast a spell. Since the amount of mana you spent is greater than the creature's power, increment will trigger. While the increment ability is on the stack, an effect gives the creature with increment +2/-2, making it a 3/1. When the increment ability resolves, the creature will still get a +1/+1 counter since the amount of mana you spent is greater than that creature's toughness.

Ambitious Augmenter's last ability doesn't cause you to move counters from Ambitious Augmenter onto the Fractal token. Rather, you put the same number of each kind of counter Ambitious Augmenter had when it died onto the Fractal token.

An increment ability will only trigger if the permanent it's on is a creature. Similarly, if the permanent is no longer a creature when its increment ability resolves, the ability won't do anything.

The increment ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack.

If increment triggers, the comparison will happen again when the ability tries to resolve. If the amount of mana spent to cast that spell isn't greater than either of that creature's stats anymore, the ability will do nothing.

Whenever you cast a spell, check the amount of mana you spent to cast it against the power and toughness of the creature with increment. If the amount of mana you spent isn't greater than either of that creature's stats, increment won't trigger at all.

Ambitious Augmenter's last ability puts all counters that were on it onto the Fractal token, not just its +1/+1 counters.

In some unusual cases, you may end up putting the appropriate counters on more than one permanent. For example, if you control The Ozolith (a card from the Ikoria: Lair of Behemoths set) when Ambitious Augmenter dies, you'll put the appropriate number of each kind of counter onto both The Ozolith and the Fractal token.

If more than one token is created by Ambitious Augmenter’s last ability (because of the effect of a card like Anointed Procession, for example), put Ambitious Augmenter’s counters on each of those tokens.