Is one allowed to fix a chair on chol hamoed that the screws fell out from? (That he needs for guests)
If he needs the chair for guests, this is tzorech ha-mo’ed, and it is permitted to fix the chair.
The reason for this is that placing back screws is a ma’aseh hedyot, and not a ma’aseh uman, and therefore no prohibition applies where there is a requirement for the mo’ed.
See Shulchan Aruch and Mishnah Berurah 530 and 533.