You're using the present perfect tense in the first, and the present perfect progressive in the second.
present perfect tense
1. "We have eaten breakfast together every morning since our honeymoon."
This means that as a married couple, you and your spouse have never spent a single breakfast alone from the first day of your marriage to now, the present day. The action is repeated, and does not exclude the fact that having breakfast together requires a certain duration of time.
Perfectly acceptable, although an unlikely situation if the marriage is longer than six months. (I'm joking!)
Present perfect *progressive/continuous* tense
2. We have been eating breakfast together every morning since our honeymoon.
Literally, this could be interpreted as both of you eating breakfast non-stop since day one of your marriage.
This of course does not make sense; however, the fact you have inserted ever morning means the action is being repeated, it is not uninterrupted as it could appear at first glance. You need to avoid this ambiguity, native speakers will tend to do this automatically without thinking.
Opting for:
Present perfect
"We have eaten breakfast together every morning since our honeymoon."
or
Present perfect
"We have always had/eaten breakfast together since the day of our honeymoon."
or
Simple present
We always have breakfast together, ever since our honeymoon.
(Insert always to emphasize an action is repeated regularly).
It's perfectly OK to follow the past tense, finished, with either past or present perfect in speaking of your subsequently becoming a teacher; but you have to make up your mind whether you are talking about what happened in the past or about where you are now.
If you use then (or next or after that or in 2007) you are speaking of the past event and must use became. Use this if you are building a narrative, describing a sequence of events—which may eventually lead to the present, but doesn't have to.
If you use the present perfect you are speaking about your present status; you cannot use then because you are speaking about now. (You may, however, say since then.) Use this if your discourse is finished with speaking about past events and will now focus on the present.
Best Answer
"Finished" is correct because it is the Past Simple.
"Have finished" isn't correct because it is the Present Perfect. An hour ago is in the past (a past time) and isn't connected to the present anyhow. If it were still happening it would be correct.
Example: