Black spots sounds like some sort of a disease.
Does the black stuff come off easily or is it inside the leaf?
It could be that you have some sort of mite or other pest. Inspect your tree carefully, especially the undersides of leaves. Are the leaves sticky?
If you know a good garden shop it might be best to take a leaf and show them. You can probably get this under control by spraying, but then you should better not eat the fruit for a season just in case you're poisoning yourself too.
Curled leaves normally have one of two causes. These are either too much or too little water. When you repotted the tree, did you take care to put in adequate drainage? Are you watering too much or too little.
Also check the pH of your soil. You may need to add nutrients or minerals.
Are these long branches you are concerned about coming out of older branches, or directly from the main stem? If they are coming from too low down they may be from below the graft which means they won't fruit for a number of years, but the quality of the fruit will still be okay (citrus grown from seed is almost always true to type, although most garden centres vehemently deny the fact because it hurts their business). If you don't want to wait that long, cut them back.
If they're not that type of shoots, just be patient, sometimes citrus trees just go through phaes of strange growth and then recover.