It has been raining all night and the wood is thoroughly wet. I want to screw on the ceiling plates (and apply the epdm on it). It doesn't seem like a good idea to my, because wood expands when it is wet and when the wood is dry again and shrunken a bit, there will be margin between the beams and the plates right? It's Douglas wood.
There is no real harm in proceeding with the deck. The wood is a bit wet, but will dry out from air movement in short order with no real risk of mold or other damage occurring. This type of structure is quite flexible and will easily absorb any movement from swelling or shrinkage (which will be very minor anyways). Wood framed homes and other structures often get wet during construction and the work recommences as soon as the rain stops.
I wouldn't if you can wait. It would be better to let the wood dry out before you work on the roof further.
You shouldn't worry too much about the wood itself as wood won't normally get damaged by being wet like this over a limited timeframe. And you don't have to be overly concerned about the structure, although ideally you protect any part-built wooden structure with tarpaulins or plastic sheeting in case of rain it's very common for roof framing to get wet during building work in any wet climate. It doesn't seem to affect the strength of the finished roofs, at least not enough for it to be a problem.
It doesn't seem like a good idea to my, because wood expands when it is wet and when the wood is dry again and shrunken a bit, there will be margin between the beams and the plates right?
Wood expands and contracts across the grain, there's virtually zero movement along the length of a board.
The reason not to do this is ideally you shouldn't drive fasteners into wet wood, particularly nails.