From your first posting…
Start here: https://en.wikipedia.org/wiki/ICalendar
1: If it is a valid iCalendar ICS file attachment invite, yes.
2: Apple IDs are not relevant here, save that many are also email addresses.
“I have some issues” is true of us all, alas not something we can address without rather more detail.
From your second posting…
Add-on anti-malware apps, add-on security apps, add-on cleaner apps, add-on VPN apps, or other such apps, installed here? Those can and sometimes do get in the way, and in unexpected ways.
iCloud is not related to this issue, save that you can enable and create and use iCloud Calendars, which are stored in iCloud, in addition to local calendars.
How this message arrival works, in very rough terms:
- Embedded ICS attachment arrives via mail
- scanner in mail detects ICS, and parses it. Or it’s mis-formatted or gets mis-parsed, and 🤮
- Mail passes the ICS info to Calendar
- Calendar offers the invite.
- You accept or decline, and an ICS file is generated and sent to the originator.
What seems to be the question…
Reading through all of what you’ve posted, it’s from step 5 onward that’s somehow messed up here; that the person that sends the invite is not receiving the response.
Have they checked their spam folder, and their message-processing rules, and their spam settings?
Do other folks from other mail providers also sending invites also not receive replies triggered by your invite responses?
There have been issues with receiving responses in some other mail and calendaring tools, too: https://answers.microsoft.com/en-us/outlook_com/forum/all/outlook-calendar-invite-no-response-required/546efb04-02af-4fec-8644-2cd805ac7c29
Which means you’re going to need to do some troubleshooting and some debugging, and try some different combinations with the sender. As this might well be the sender’s problem, not yours. Have them try the web calendaring interface, or some other tool (same as the earlier try-a-different-sender), for instance.