The folder should not be asking for any type of local authentication if all you did was enable web access, however if you have also enabled access restrictions on the folder it will. In order to work around getting prompted for login credentials everytime you access the folder in this case you would want to map the network drive rather than just navigating to it every time. In order to do this after you navigate to that folder right-click on it and select "map network drive" and it should show under My Computer with whatever drive letter you assigned.
As for the firmware, updating should not cause any data loss since the firmware is written to a part of the drive separated from the data sector.
The fastest method to transfer to USB would be through the disk backup feature within the Linkstation's configuration page as this will take the throughput of the PC out of the equation. As for the function button issue, this isn't anything I've seen before, what make and model USB drive are you using with this?