A few questions about the Famicom/clone keyboard

[Satoshi_Matrix]

1) Is the above photo taken from an official Nintendo (word processing?) program that is being ran through a Famiclone or is it pirate software? What is it called?

This is from the "memo" program on the Family BASIC V2. The Family BASIC was a keyboard and software creator that allowed users to write their own simple games in HuSharp BASIC and then play them. Individual parts of Family BASIC have been taken apart and left as if they were full programs, such as this here. The main purpose of Family BASIC was to write your own programs and then save them to either cassette tape or to an internal battery.

2) The above photo is obviously just a screenshot, but is there any way to browse the internet on a Famicom, famiclone, or any 8-bit computer for that matter?

Well...not to confuse you, but the Famicom DID get a modem in Japan that accessed a server that provided game cheats, weather forecasts, live stock trades, etc, but nothing like a web browser. There is no way for a Famicom or Famiclone to access the internet. The Commodore 64 is the only 8-bit computer to do that to my knowledge.

3) Is there a PC program that emulates this Famicom word processor?

No. Again, this isn't a word processor, this is just a temporary memo pad that was part of the Family BASIC V2.

4) Does a mod or adapter exist that allows a Famicom keyboard to hook up to a PC?

No.