These two sound a bit weird without any context, but they could be fine. Where is the first speaker now? Is the second speaker leaving an eleventh message on an answerphone? (If so, the present perfect would be fine)-I've seen many videos at the police station.
-I've left you 10 messages!
Again, it depends- if the problems are ongoing or very recent or there are likely to be more, the progressive form is fine. It could also be used when explaining something to the person who has come to repair it, for instance.-We've had many problems! (Would it be better to say: We've been having many problems!).
Student or Learner