If I recall correctly, you can only use 1 room at a time in the first year (e.g if you have 2 production rooms in the first year, only 1 room produces each production step).
This is not correct. If one has enough imps, one may "power up" all rooms in year one.
In year two, each room may produce double, but only if the rooms receive enough imps. (A "gold" room will produce 2 gold if supplied with 6 imps.)
Also, room production is instant I presume? Consider using a food production room and immediately using that food to buy an extra imp (in year 2)?
Yes, rooms may be powered up in any order, and the output used to power another room, if desired.