by gillum
The rules for the Construction Firm state explicitly:A player can take both buildings from the same pile. A player may even use the Construction Firm to build one building, then use an additional action to buy the next building, and then build the third in the pile with the Construction Firm.
With regard to selling, I'll point out at the rules say "Additional actions are Buying and Selling, which may be carried out at any time during the player’s turn."
I would say that the ability to buy a building while using the Construction Firm is just an application of this general rule. That would imply that you can also sell a building at this time.
I think that the only difference between buying and selling (with regard to timing) is that you can sell but not buy during another player's turn(if you sell during another player's turn, you cannot do so while he or she is taking an action).
But during your own turn, you can sell at any time at which you are allowed to buy.
Of course, "Buildings may not be sold and then bought again in the same game turn."