Is the obligation of Friday prayer waived for someone who prayed the Eid prayer if Eid falls on a Friday, and does this ruling apply to the rest of the prayers on other days?

If Eid and Friday coincide, the preferred view is that whoever attends the Eid prayer is granted a concession to skip the Friday prayer, but they must pray Dhuhr in its place. However, if Eid falls on a day other than Friday, then the Dhuhr prayer should be performed in congregation as usual, unless there is a valid excuse preventing it.