I don't believe the fuel circuit is that complicated. As you prime the bulb, surely it is simply drawing / sucking fuel from the fuel tank. There is no pump on the fuel tank itself so fuel is sucked to the front of the car by the engine mounted fuel pump. However there is something certainly wrong if you are finding air in the fuel pipes at all. There shouldn't be air in the system unless there is a leak or some other fault.
After the fuel filter, as far as I can see the fuel goes directly to the fuel pump. After passing through the fuel pump it returns to the fuel filter and is filtered another time (reason for four pipes at the filter) then off to the fuel injection system. There may be a non-return valve and other components but as far as I am aware that's the basic circuit.
Another point, you should not be needing to use the prime bulb. Most cars didn't in the past have prime bulbs. The prime bulb is only there for the purpose of filling an empty fuel filter after a new one has been installed. Otherwise you would have to manually pour fuel into the filter and fill it yourself when fitting a new one during maintenance.
Further to my above post, did you have your car serviced in recent times and a new fuel filter installed?
If so, it might be worth checking that the four pipes have been put back onto the fuel pump in the correct order.
1. Note AHTO42s earlier point: -
'Fuel return pipe. There is a valve that puts the injector return system under pressure. When the valve fails, then the engine is hard to start.'
I believe this is a non return valve, I would have it checked. The way you describe the problem as being very intermittent would remind me very much of a sticking valve that sometimes sticks, then frees up again. Pumping the ball perhaps frees it for a while?
AHTO42s English may not be great, but he is probably the most experienced member on this site with regards to the T31 X-Trail and is his comments are usually accurate.
2. Were it not for the intermittent nature of your fault, I might have also suggested timing chain slipping a cog. The car will run with minor issues one cog either side on crank shaft sprocket. It will even run two cogs either side albeit with starting and other issues. I have discovered this during research on my problem described also on this forum. Timing chain guide tensioners appear to fail around 100K to 120K miles rendering chain loose and vulnerable to jumping cogs.
Bus-man - read my latest discussion about timing chain on my other topic about whether I should fix my car after timing chain tensioner issue. At the end of the day, timing chains should be much less likely to give trouble than timing belts, providing of course that car is not abused and oil changes are done at intervals no longer than Nissan suggests, and that good quality oil is used.