First, the trimmer head should not rotate when you pull the starter. You may not have correctly assembled the engine back onto the drive shaft. The centrifugal clutch is in between the two. It usually consists of a pressed steel drum on the shaft, and a centrifugal mechanism on the engine.
Second, there are several versions of how to vent the fuel tank. Essentially you either have a vent in the tank cap, or a tube extending from the tank. If you have the tube system, it should not have fuel in it but you may have made this happen by overfilling or something of that nature. It is probably not the source of your starts-and-then-stops problem.
Third, the normal and recommended technique for cold-starting brushcutters or chainsaws that have a choke and no primer, is to pull them over with the choke closed until they start and then immediately stop, then open the choke to about two thirds closed, and pull the starter again. Unless there is something wrong, they will then start first pull and run through warm-up, during which process you open the choke the rest of the way. Those engines cannot run with the choke closed: they do not have an "unloader" on the choke, so they are simply strangled to death immediately. In the process of strangling and dying, they pull fuel into the crankcase so they are then able to start very easily on the next pull.
