Should bicep curls be done separately or together??!

Should bicep curls be done separately or together??

I have been doing free weight barbell bicep curls together, and I have noticed that my left arm is a little weaker then my right (like when I do my bench presses).

I am currently curling together at 70 lbs, so I would have to put 35 lbs on each dumbell.

Also, should they be lifted as in a "running" motion with the palms facing each other, or should they be lifted with palms facing upward? Which would work the biceps more??

You can do more weight if they are done separately with dumbells. Doing them together with dumbells is harder and might give you the better workout. But if you are doing barbell curls before, you might want to do them separately. Maybe do them on a preacher curl bench from time to time. Palms facing upward are harder than palms facing each other(hammer curls). Hammer curls work more of your forearms and the peak of your bicep. Palms upward or just a regular curl work the overall bicep, and not as much forearm.
To make your left arm as strong as your right try this: If you curl a 35 in your right arm try curling a 40 or 45 in your left arm at the same time. Just do this maybe the last set or two when you do dumbell curls. Don't do it on barbell curls, the weights might come off the side unless you have clips. Also train your forearms. The stronger your forearms, the more weight you can hold onto. Try to strengthen your front deltoids(shoulders) and your triceps to help your bench press. Military presses with a barbell or front raises. Do some dips or french presses for your triceps. Don't go heavy, try to do it with good form with less weight. If your sore the next day, your doing it right.