A player puts a power plant up for auction. Is that allowed if he doesn't have enough money to buy it himself?
No he is not.
According to the rules (Pdf):
The player chooses one power plant from the actual market (top row) and then makes a bid to purchase it (the player must bid at least the minimum bid (number of the power plant), but may start with a higher bid.
The player starting the auction must start with the opening bid.
If he wins the bid he must pay the bank:
He pays his highest bid to the bank and takes the power plant.
This implies that one must have enough money for the bid.