> Does it work to simply give them a trial extension with extension length of 14 days? So considering they have used the trial beginning of August, ran out mid of August and reactivate in October.
Yes.
> What does the "Expiring date" do?
The last possible day the trial can be applied (i.e. the last possible day the user can physically put the trial extension in the "trial extension" textbox and press the "OK" button).