The oil that fills the dashpot is there for dampening, controlling the rate at which the piston can rise in response to engine vacuum. Lack of oil can create driveability problems for some cars and not others. The original SU oil from the factory would have been a straight 20W. You will see people using everything from WD-40 to gear oil. I would start with 20W and see if things improve.
There have been numerous threads about how much oil goes in the carb. The real answer is... with the black damper cap removed, look down into the top of the carb. You will see a steel tube in the very center. That's where the oil goes. Stop filling when the oil gets to about 1/4" below the top of that innermost tube. Any more oil than that will just get sucked out and burned.