I urgently need you to check these sentences, Writeacher. Thank you very much.

1) I was invited by Mary to come round (come along is possible?) one of these days.
2) You ought not to worry about (or be worried about but NOT be fussed about?) a common (not a normal?) cold/about the result of your exams (also exams' result?)
3) She excused herself to me for breaking the vase.
4) She invited me to her house one of these days.
5) I remember leaving (also: forgetting?) my keys on the table last night.
6) They are disappointed with (is "by" a mistake?) their exam result.
7) He hurt his knee when he fell off the raft.
He hurt his knee falling off the raft.
He hurt his knee when he fell off the raft.

1. ... to come around ... (correct)

("to come along" means someone needs to catch up to the others as they walk or drive or otherwise move forward - this phrase implies that the person who needs "to come along" is going too slowly.)

2. "fuss" doesn't work in this context; forms of "worry" are fine.

3. delete "to me" (Haven't I already typed this before??)

4 - 7 are all fine. (Either "with" or "by" work fine in 6.)