If the situation is as you describe, that you wiped over your socks after having put them on when you were not in a state of purity, because you were unaware that that was required, then you do not have to make up those prayers according to the view of a number of scholars, but if you are able to make them up, that is better and is more prudent.

You can do wudu with socks on if the socks have been put on when you are in a state of purity and they are pure, and the wiping may be done within the time specified by Shari`ah.

This is how to wipe over socks in wudu: put your wet fingers on the toes then pass them over the feet to the shin; the right foot should be wiped with the right hand and the left foot with the left hand. The fingers should be spread when wiping and it should not be repeated.

Intention is not required for wiping over the socks to be permissible as long as they are worn in a state of purity.

Wiping over the socks is limited to one day and one night for the non-traveller, and three days and nights for the traveller.When the period ends, it is not permissible to wipe over the socks until you take them off, then put them on after purifying yourself fully with water. You can overcome the difficulty of washing your feet by sitting on a chair, or pouring water over the feet without bending down to wash them.

The time for wiping over socks may expire but your Wudu remains valid as long as you do not perform any act that breaks it.

If the time for wiping over the Khuff has ended, and you have Wudu, then your Wudu does not become invalidated according to the correct view. If a person takes off the Khuff or socks after wiping over them, his Wudu does not become invalidated according to the correct scholarly opinion.