Viewing Special Characters
The good news is that this part should almost always 'just work' on OS X and iOS devices. Encodings are usually handled intelligently, Unicode fonts are installed, and font substitution does its job.
If you do encounter problems, be sure to specify the encoding as Unicode (UTF-8)
when saving. If your text editor doesn't allow you to specify an encoding, it's a fairly safe bet that this is what it's using.
Since Markdown files are plaintext, you don't have to worry about fonts. If you are using rich formatting, though, Lucida Grande, Arial Unicode, and Apple Symbol are all good options. But, again, OS X and iOS generally switch to another font seamlessly when the main font doesn't support a character.
Entering Special Characters
Both OS X and iOS include built-in text replacement tools that will let you insert your symbols easily.
OS X
Open System Preferences-> Language and Text-> Text and click the [+] button. Choose a keyword to be expanded and paste in the special character. You'll have to create snippets with unique keywords for each character.
iOS
Copy a special character. Open Settings-> General-> Keyboard-> Shortcuts and tap the [+] button. Paste the character under Phrase and enter a unique keyword under Shortcut. Tap save. Again, you'll have to create snippets with unique keywords for each character.
If you like, you can use the excellent TextExpander to do the same thing, but it isn't necessary in this case.
OS X normally will not display a character in the Private Use Area unless you manually set the font in the app. I understand this is intentional, since every font could have a different glyph at the same PUA code point, and it only makes sense to display something when the user specifies the font.
I think it should also work when the right font is selected via CSS or other markup in a document being read.
Some earlier versions of OS X did not have this "feature" and did display PUA stuff. I don't know how they chose which font to use when more than one had something at the code point selected.
Best Answer
You would have to add fonts to your iOS device which contain the characters which are missing. This can be done with various apps from the app store, like Anyfont.
You might try the font Symbola.