🔖
I am not sure whether everyone can see the above character, but I can see it. I got it when I input "booknote" in Chinese on my iPhone. To my surprise, this character seems "platform-insensative", it can be seen on my phones, chrome on laptop, and even in MacOS terminal.
Is it an ASCII character? I've never seen colorful characters like this before. Since when these have been around? And where I can get a list of similar characters?
Here: http://www.unicode.org/charts/nameslist/index.html
You put the character on an HTML page. All characters on an HTML page are from the Unicode character set. Characters that are not in the Unicode character set either soon will be or are too specialized to be of general use.
The Unicode Consortium occasionally publishes a new version of the character set. Since you ask about the kind of character, the common partitions of the character set are blocks, categories, and—stretching a bit—which version the character was added in. Some characters are in a script (for a language writing system), some are not. You see the block and category of 🔖 at http://www.fileformat.info/info/unicode/char/1f516/index.htm.
The Unicode character set is published in text files called the Unicode Character Database (UCD), as well as many supplementary documents and webpages. The data includes important information about usage and relationships. For example, for applicable characters, which character is considered the uppercase form of another in a particular language.
To see any character, you have to use a font that presents it. This can be a problem for some characters. There is probably no one font that presents every Unicode character as it was meant to be.
You mentioned ASCII. Although it used every day in HTTP headers and other specialized and historical applications, ASCII is such a limited character set that it hasn't generally been used in decades.