Ответ:
1. I see no obvious reasons why we should reject this offer. (не точно)
3. I was gaining progress slowly but steadily.
4. Eventually, I was able to reach the top of the list. (про ..and хз, либо перед eventually)
6. We are likely to fall behind as we are making a little progress.
7. Could you possibly advise me on the apps I can use for studying?