Whether or not it is a true English word and where it came from are two completely different questions. We borrow words from many languages, but they are still real English words.
It is borrowed from Swahili [safari], which was in turn borrowed from Arabic [سفاري].
It has been attested in dictionaries as part of the English language since c. 1890.
Etymology
The word nan for grandma is a shortening of the word nana. Both of these words probably are child pronunciations of the word nanny. Etymonline describes this word as originating as a child's word for "female adult other than mother". This is why nanny is used as the word for a caretaker of children (since the 18th century) as well as a grandmother (since the early 20th century). Etymonline also notes that nanna is also a Greek word for aunt.
Grandma has similar origins. The word mama is a child's form of mother. In languages like German and English, the parents of one's parents have the grand- prefix applied to create their names. The original form of grandma was grandmama (18th century, OED). So this is simply the result of applying the grand- prefix to the child word. Then, like ma was derived as a shortening of mama, grandma evolved from grandmama.
As you can imagine, dad and pa/papa are also child words for father.
Why have multiple words
The reason there are all of these names is the same reason why most of us have nicknames for certain people or things based on childhood pronunciations. Whether that means calling your blanket a banky or your sister sessa, most of us form an emotional connection to things from this time period. Even the alternate word for stomach, tummy comes from a child pronunciation. Child language becomes a major part of family life for years, and it makes sense that some words are extended beyond the domain of early childhood development.
We retain these different forms of these words for at least two reasons: (1) each of us gives these words a differing level of significance (who wants to replace the word they use for their loved ones?) and (2) we often have different words for things that we individually use that are appropriate for different registers, e.g. kitty, cat, and feline.
Best Answer
'Hey' ( perhaps originally a natural expression) appears to be at the origin of 'hi', while 'hello' seems to have no connection with the previous two terms and a different origin (mainly as a telephone greeting).
Hello :
source: Etymonline.com