Hi blancheRV,
Thank you for using Microsoft products and posting in the community.
I realise that you are experiencing a calendar related problem and I will do my best to help you!
May I ask what your email domain is? Is it a Microsoft domain email? Or is it some other third party email address?
Allow me to explain to you that if you are using IMAP protocol then IMAP protocol does not synchronise calendars, which means that if you add a calendar in new outlook then you won't see the calendar event on the web side because it can't be synchronised to the web side.
Before answering your question, I did a test in new outlook, in general, if you yourself as the invitee of the event, then you can edit/delete and so on, if you are the invitee of the event, then after you receive the email of the event invitation, you are able to choose to agree/deny/tentative. But your problem is that you can't perform the appropriate actions whether you are the inviter or the invitee of the event, please point out if I have misunderstood.
My test result is that I can edit my own event and at the same time can accept/decline other people's invitations as the invitee of the event. Although I didn't reproduce your problem, some remedies I can think of for you are: if you're editing your own events, you can check if your calendar is under your own account and tick [My Calendar] to see if there are some calendar categories etc. Another aspect is that you can check if your calendar event is a regular calendar or a shared calendar?
If the problem still exists after you try some methods, I recommend that you look for Outlook support online. You need to click [Help]-[Help] in the taskbar above the web version of Outlook, a help interface with a search box will appear on the right side of the web page, if you see an almost empty interface with a backlink in the middle, click [Help] again. If you see an almost empty interface with a backlink in the middle, click **[**Help] again. You need to type [Events in New Outlook can not be edited, deleted, or created] in the search box and then click Search, once the search is complete, a **[**Need help yet?] Click [Yes] to be redirected to the Outlook online support page, click [Chat with Microsoft Support on the web]. Here you can find Outlook Online Support employees.
Thank you for your patience and support.
I wish you all the best
Vivian - MSFT | Microsoft Community Support Specialist