Just had your second problem, in my case it was a faulty earth strap. Put a new one directly from the battery to the gearbox, and all is fine.
About your first problem, i would guess its air, check the return pipes on the injectors, as i had a similar problem with my dads 110, 300tdi. Found one of the pipes cracked and it sucked air in on starting then leaked ever so slightly while started, was rather difficult to spot, but after i changed the pipe it never did it again.
G