The library, amazon.com, or if you have a kindle/ nook from the store located on the kindle/ nook
Yes
You cannot search the web on the nook simple touch. But if you want to search internal library, there's a search box in the library.
if you go to your library on the nook at the top it will say "shop now" in blue letters. if you click on that it will take you to the nook store. there you can search any book or app you want.
There are many different websites to download nook books. Some sites are free such as local library sites and others will charge fees for the nook books.
Yes if the library has wifi access.
I am not sure how to do this from the Nook device itself, but I have found the borrowed items in my master library at BN.com and returned them from there.
yes, libraries usually use epub or pdf files as the format for their ebooks, both of which are supported by the nook
you go to the barnes and noble website and sign in to your account (the same one that is registered onto your nook), and then you go to my account, then my NOOK library. that will bring you to a page where you can delete any of the books off of your nook.
Yes, if it is jailbroken.
Go to your library and ask them about it. They will tell you what to do.
It may be possible, but it's not easy. You have to get root access and install a web browser. The method for getting root access is tricky and depends on the Nook version. Using the wrong technique to gain root access can render the device unusable.