Could we build a pyramid in the Central American jungle without our power equipment?

Yes, though we wouldn't want our rulers to have the power over us implied by that.


Carve and raise the heads on Easter Island?

Little problem. Motivation is the only issue. Easter Island was a prime example of willy waving run riot, and they ended up destroying their own ecological system.

Create a base 12 mathematics system from scratch, much less one in base 16?

1, or 0x01 perhaps.

Create buildings as astronomically precise as Stonehenge, Woodhenge, and tombs of the Boyne Valley?

Yes, and far more precise, and regularly do.

Create and sail craft to populate Oceania? Create a culture that not only survives, but flourishes, in the Arctic?

People have done that not once but several times independently, BTW. The main thing stopping marginalised people from learning to survive in inhospitable environments today is mass communication and restrictions of movement, plus the fact that the numbers would soon overwhelm the resources available.