Powering the merchant room, should I do it? How can it assist me? It's not really clear because I can trade with the merchant even though his room is un-powred.
Aslum's answer is incorrect. Powering the Merchant room doesn't generate Dust. It only helps you to build defenses to protect the Merchant.
Regarding Dust generation, after you have researched the Shop (Major Module), build one, at which point the Merchant will be teleported to the Shop. Afterwards, if you select a hero to Operate the Shop, you will gain Dust per turn.
Powering the Merchant room generates extra Dust for you. This will allow you to power more rooms, which means you can have more of the other towers going and therefore more of everything in the long run. This does mean if you find the merchant way late on a floor it might not be worth powering the room.