2. OK

3. Walked.

4. Cut

5. OK

6. OK

7. Heard.

8. OK

9. Wording is clumsy, but the tense is OK.

So, something like, “Our boss had been walking into the room when he hit the door frame.” OR “I had been walking the dog every day up until it died.”

How to rewrite #2 depends on what the sentence is supposed to mean. “I had split up with my girlfriend and was feeling terrible,” is probably best.

3. Our boss walked into the room without us noticing. (simply describes the action)

or Our boss had walked into the room without us noticing. (tells what has already happened. This is “more past” than the other example.)

4. I cut myself…

7. “Have you been hearing” again suggests continuous action–like when there’s something big going on and people keep checking the news. If there’s a single piece of news, the sentence should be: Have you heard the news…

All the others are OK.

3.Our boss (had been walking) into the room without us noticing. – Better would be ‘walked into the room’.

4.I (was cutting) myself quite badly while shaving this morning. You could say ‘was cutting’, but it would imply that you took a razor and cut yourself several times on purpose. Use ‘I cut myself’.

7.(Have you been hearing) the news today? – Better would be ‘have you heard’, unless the initial piece of news was followed by a series of related incidents.

3. Our boss (had walked) into the room without us noticing.

OR:

Our boss (walked) into he room without us noticing.

4. I (cut) myself quite badly while shaving this morning.

7. (Have you heard) the news today?

I (had cut) myself quite badly while shaving this morning.

(Have you heard) the news today?

(I have been) here for 3 years in December.