1. Not only "hi" or "ni". It can be "nichi", "jitsu", "ka", "bi" etc.
2. Yes.
Even one word can be read in different ways depending on situation. For example, 明日can be "ashita" or "myounichi".
Generally, "ka" and "nichi" are used for dates ("ka" - 2-10,20 day of month, "nichi" - 11-19,21-31. 1th day is 一日 - tsuitachi).
"hi" is often used for holydays, like "kodomo no hi" - Children's day
"jitsu" is often used in formal and honorific speech.
"ni" is used in "nihon" - Japan. "nichi" can become "ni" with double consonant after it, like in "nikki" - diary.
Don't try to learn all readings for this kanji from the very beginning. You will find reading rules later.
You can always check spelling in dictionary (i'm doing this with all new words even if i'm sure that it can't have other readings). There are a lot of words with this kanji and some of them have unexpected readings :)
http://jisho.org/words?jap=*%E6%97%A5*&eng=&dict=edict&romaji=on