First, regarding the issue with you not seeing starred status between Aquamail and Thunderbird.
I just checked that the toggle of the starred status ("Flagged") is reflected in the other as soon as the other e-mail client synchronizes. (If you have IMAP Push in Aquamail and "Allow immediate message notifications when new messages arrive" in Thunderbird, and the IMAP server supports IMAP IDLE, then it happens almost immediately. Otherwise, as soon as the scheduled sync happens. You can also sync the account/folder manually.) And I believe both e-mail clients in question correctly implement the standard (RFC 4551) that defines how the flags are set and transmitted between the servers and all clients.
So, I suspect that you might not be waiting long enough (or not synchronizing the client in which you expect to see observe the change manually). Alternatively, something might not be implemented in the IMAP server correctly...
Now, regarding the date associated with the \Flagged (starred).
I am not using Outlook, but in both Aquamail and Thunderbird (IMAP), tagging a message with a star does not do anything date-wise.
AFAIK, in IMAP standard (
https://tools.ietf.org/html/rfc3501 ), \Flagged (which is what set when tag a message with a star) does not have any date attribute.
I see that in Exchange, however, there is an attribute "FlagCompleteTime".
So, e-mail clients connecting via IMAP have no way of receiving or transmitting any date information. So, whatever date is associated with the "star" (if any) is would be the initiative of the server, and then Outlook (via one of the Exchange protocols (EWS?) ) would get that strange date.
How Outlook itself sets the date, - I have no idea.
Having said that, now, I am thinking that some of the later RFCs that define extensions to the original IMAP 4rev1, might have defined the attributes (e.g. I see RFC4466 defines some messages metadata: append-opts = [SP flag-list] [SP date-time] *(SP append-ext) - but I am not sure which metadata that includes...
Kostya when he gets to here (probably tomorrow) will have more information about this, and he would definitely know how Aquamail is programmed to behave with respect to the stars and related dates.