You can always activate an ability that will cause a creature to adapt. As that ability resolves, if the creature has a +1/+1 counter on it for any reason, you simply won't put any +1/+1 counters on it.

Incubation Druid doesn't care about any restrictions or riders your lands put on the mana they produce, such as those of Unclaimed Territory and Guildmages' Forum. It just produces one mana of the appropriate type, with no restrictions or riders.

If a creature somehow loses all of its +1/+1 counters, it can adapt again and get more +1/+1 counters.

The types of mana are white, blue, black, red, green, and colorless.

Incubation Druid checks the effects of all mana-producing abilities of lands you control, but it doesn't check their costs or legality. For example, Spire of Industry says "{T}, Pay 1 life: Add one mana of any color. Activate only if you control an artifact." If you control Spire of Industry and Incubation Druid, you can tap Incubation Druid for any color of mana. It doesn't matter whether you control an artifact, whether you can pay 1 life, or whether Spire of Industry is untapped.

Any change to a land's type or abilities gained by a land can affect the types of mana a land can produce.