Like T3sl4co1! said, those (tapatalk emojis) are images. Unicode has some, too.
Depends on the browser/os combo i think..
No. Some forums use images, or map the Unicode characters to specific images, so it depends on the forum. If Unicode emojis like 😲 are used, their visibility depends on the Unicode coverage of the font used. So, it does not really depend on the OS.
On my Ubuntu 16.04.4 LTS (two years old, so not "cutting edge") system, the salient tables on the Wikipedia
Emoticons Unicode Block look like this: