Dear ScudderB,
Good day! Thank you for posting to Microsoft Community. We are happy to help you!
Based on your description, I have probably sorted out your question:
- In your Outlook for Mac, you can't send messages normally because your reply, forward, and reply all buttons are grayed out, and it seems that they are invalid.
- How did you know about the two conclusions you mentioned from your own research? Maybe you're seeing some error message or error code? If so, please share the screenshots with me so that I can do more research.
- About the outlook search problem, this is a hot issue, because the problem appears in the server backend, Microsoft has carried out a repair, the current problem has been fixed, about the repaired situation, please refer to the official documentation to give the instructions: New Outlook for Mac stops responding when using the search feature
- About the "no OLM import function in the "New Outlook" version you mentioned" As I know, the Exporting/Importing of .olm and .pst files feature is not currently supported and is in active development. For references: The new Outlook for Mac.

If you need to import the .olm file to Outlook for mac, it's suggested that you could try to switch back to the Legacy Outlook to use this function.

In light of the questions I listed above, my suggestions are as follows for you to try and then give me feedback on the results so that you can help me narrow down the problem:
Please try logging into OWA (outlook web app) with your account to check if you have the above problem.
Please try to rebuild a test profile on your outlook client to check if these problems will still occur, please kindly refer to it: Create a new profile
Also please try to reset your account to check the result: you need to quickly remove your account from Mac Outlook and then add it again. Follow the steps below to reset your account. First, open "Outlook" and go to the "Tools" option> now, select the account from the tool options> select the account you want to remove from the account settings> click the delete button and confirm that you have chosen to delete the account > delete the account, launch Outlook again and add the same account details to reset it.
I know that the above questions are very confusing to you, and we apologize for the inconvenience caused to you, but I still ask you to give feedback on the methods and questions I have provided to you, which will be very helpful for us to do further research, thank you for your support in advance!
Thanks in advance for your understanding! Your patience and cooperation will be highly appreciated. Hope you all the best!
Sincerely,
Kerry Chen | Microsoft Community Moderator