Not really sure what "jumping" means in your description, but none of the things that you mention should cause the bar and chain to cut poorly or erratically, if all the cutters on the chain are sharpened at the same angle, 30 or 35 degrees, and cutters are relatively even in length from side to side. The original bar or not or a few chain anomalies shouldn't cause problems if you are using things that are designed to be operated on that saw and are in proper combination with each other. Is your sharpening leaving you with a sharp chain or have you done anything to leave yourself with improper raker settings that cause a grabby chain? Sprocket teeth count shouldn't be a factor unless you might have something very strange on there that doesn't belong. Inspect all parts for damage or excessive wear, and when sharpening, make sure you are using the correct file size for the specific chain. If you are using way too large or too small a file compared to what is recommended, I suppose it could mess things up so the chain won't slice cleanly through the wood. Especially too large a file would probably yield blunt cutters that want to bounce on the wood. Is the chain sliding in the bar groove correctly or any damage to the end of the bar where the tie straps get engaged? If you can't sort out the problem, you should take the saw to your dealer for a look over. A trained eye should quickly figure it out.
