In my opinion you need to use a ridge beam and keep the pitched roof. You need to find what kind of live loads you roof will need to tolerate, particularly snow and ice loads.
Once the roof live load is considered, that gives the info on what is needed for the building of the ridge beam.
A ridge beam is different than a ridge pole.
A ridge pole is a single member where the roof rafters make their attachment at the peak. It can be of 1X material or 2X material. It helps the framing maintain a straight line and adds some structure, but collar ties or ceiling joists are still required to reach potential strength, along with proper nailing.
A ridge beam is made up of numerous 2x material an eliminates the need for ceiling joists or collar ties. Whether the beam is made up of 2, 3 or even 4 pieces of 2X or perhaps a lesser number of LVL or PSL members is figured by design loads, the amount of weight the beam needs to carry over its span. Also the area where the beam rests on the walls will need additional studs under them for there will be tremendous pressure in those 2 places where they bear. If there is a pier under there, it needs no more. If there is no pier there, then a beam needs to be placed in the wall either high at the top plate or low at the bottom plate to span over the closets piers.
About your door. The door is in a non-bearing wall. The header you have can be much smaller since there is nothing but the possible sag of the roof rafters along their span that may cause an issue. Using a continuous piece of plywood over the door to act as a diaphragm will minimize that potential. Plywood on both sides is great assurance.
About the pitch of your roof, again depending on the snow and ice loads a 1 degree pitch is not enough. By the time the roof sags under the weight, I fear the water will puddle in the sag. A 5 degree pitch should remedy this problem. The more the better.