Pro tip - I answer messages to the User Group based on the oldest message I see that has not been replied to.
By asking for updates you're actually delaying me from getting your messages :)
If no one has replied for over a week then yes, it is worth asking for an update in case its slipped through the net.
I would advice against using the same session file - it will just keep growing and will take longer and longer to load (we have an open issue about that;).
To be honest I'm a bit confused by what you have said
If you have applied code fixes then that implies they were True Positives, not False ones?
If they are True Positives then you should not mark them as False Positives.
If you have fixed them properly then ZAP should not raise new alerts when you test the fixed code.
For real False Positives, as per the FAQ - let us know the details and we can hopefully fix them:)
If not then you can just configure Alert Filters to automatically change them to false positives.
In the desktop just right click on the alert and "Create Alert Filter...".
You can create global ones to apply to everything, or context ones and then save the context. You can then load the context when you restart ZAP.
Cheers,
Simon