What should I do if, during prayer, I remember that the period for wiping over the khuff has expired? And does my ablution become invalid if I wore socks under the khuff while in a state of purity, then removed the khuff and remained with the socks?

The preponderant opinion is that the expiration of the period for wiping over the khuffayn (leather socks) or their removal does not nullify wudu' (ablution). Rather, ritual purity is nullified only by the known nullifiers. Consequently, if the period expires or the khuff is removed during prayer, it is permissible to continue the prayer until wudu' is nullified. Upon removing the khuff, it is not permissible to wipe over it again except after a complete purification by washing the feet.