There is no driver for Windows 8.1. Did you try the one for Windows 8? http://www.tp-link.com/en/support/download/?model=TL-WN821N&version=V3#tbl_a

The original one is faulty or you just want to get a spare one? As I know, the battery is not for sale. But you may confirm with TP-LINK support... For Support in India (English & Hindi Service) Call...

Have you solved it? :) Ensure WLAN AutoConfig is enabled or try to connect using Windows bulit-in utility directly. http://www.tp-link.com/en/article/?faqid=306

There is a chipmaker's driver(AR9271) for Windows 7 to update. https://www.atheros.cz/atheros-wireless-drivers.html

Umm...maybe try to call them or email them directly?

Are you trying to search for Wi-Fi name of the router? How about WLAN light on it? Try to hard reset it. Can you see a Wi-Fi named TP-LINK...? You can use a cable to connect your PC and WR841 to see...