No because cailín (girl) is masculine in Irish. It's only feminine nouns that begin with a consonant (other than d, t, s) that are lenited after the definite article.
- an mhairteoil = the beef
- an chloch = the stone
- an fharraige = the sea
- an madra = the dog
- an cóta = the coat
- an fear = the man
Yes :) Don't think of masculine/feminine as being related to male/female.
an is singular (except for feminine genitive) and na is plural. It's similar to the difference between French le/la and les
yes. It's the English spelling of Caitlín, which is an Irish form of the name 'Catherine'. It doesn't come from cailín, though the name Coleen does.
It depends upon the particular device that you use and which operating system it runs. For example, under OS X, one would hold down the Option key while typing “e”, then release the Option key, then type “i”.
It can also depend on the keyboard. On a Scandinavian keyboard in Windows you press ´ (it's between + and backspace) and then i to make í.
Proper nouns (e.g. names, titles, etc.) do, but common nouns don’t. It’s not like German, in which all nouns need to be capitalized.