Logs from Messenger Plus! are either text (TXT files) or HTML logs and are already saved as such.
You can use Internet Explorer to open the HTML logs or the build-in LogViewer from Messenger Plus!.
If you have enabled online logging, instead from the
webinterface, you can also read the logs from any computer using the build in LogViewer in Messenger Plus!.
(select
MyPlus! instead of
Local in the LogViewer's treeview on the left side)
Note that you don't even need to have Messenger (and thus Messenger Plus!) running to start the LogViewer. Messenger Plus! must just be installed and properly configured though.
(Plus! > Preferences & Options > Passwords > MyPlus!)
Automatically informing about log updates is not possible. And personally, I don't think something like that will be added anytime soon.