(Not a teacher)
Here are some ways to state these (there are of course other ways). Sometimes the negative works better:
1. The test wasn't that hard; At first I thought I was going to fail but now I don't think I did. (if you say "I think I did it," it possibly suggests that you did fail. Later you can say, "I did it! I passed the test").
2. I couldn't imagine I would be able to fix all those [or, all the] problems, but I did [fix them; manage to fix them; succeed]. If you just say "I did" or "I did it," the "did" can refer to "imagine" as well as "fix."
3. I don't think I'll have enough time to fix all those [or, all the] problems. I hope I'll be able to do it. Or, I hope I will have time.
5. It took me a while to get that promotion but I finally did! Or, ...I finally got it ( you can replace "get" with "receive" here so you don't use the verb "get" twice).
Student or Learner