Proper Usages of あおい

I am starting to learn Japanese using NihongoMaster.com as my primary resource. On the first lesson, the word 'blue' was translated as あおい (aoi). For quick translations I usually use Google Translate. When I use the Google Translate IME and type 'aoi' I get 青い and it is translated as 'blue'. Also, when I just type 'ao' I get 青 which is also translated as 'blue'. But when I type 'aoi' in my Windows 7 IME I get 葵 which is translated 'Aoi'. I would like to know the difference between these and the proper usage of each.
To summarise: the things I would like clarified are あおい ，青 ，青い ，and 葵 .

青: blue(noun)
青い: blue(adjective)
葵: aoi(the name of a plant. It also can be the name of an emblem, a place name, a family name or a given name.)
あおい has some more meaning other than the above (e.g. a family name 青井).

OK, this is probably totally inappropriate (and off-topic), but...

Toritoribe, you're awesome. 尊敬してますよ。因みに、ちょっと酔ってるんですけど 、気持ちは変わりません。

Toritoribe said:

青: blue(noun)
青い: blue(adjective)
葵: aoi(the name of a plant. It also can be the name of an emblem, a place name, a family name or a given name.)
あおい has some more meaning other than the above (e.g. a family name 青井).

Click to expand...

Thank you.
I have a related question reguarding the use of 「青の」; from what I understand, this can also be an adjective meaning 'blue'. What I would ask is: How would 青の be used differently than 青い ?

Note: and example of 「青の」in usage is in 青の祓魔師 (ao no futsumashi [Blue Exorcist])

The following thread might be somewhat helpful.

くろしつじ and きいろのなな - Adjective problem! | Japan Forum

青の doesn't mean the color of the exorcist is blue. It shows that he has an attribute / a characteristic which "blue" expresses. In the manga/anime, blue or blue fire is a symbol of Satan, thus, the title suggests that the protagonist has something to do with it. (In fact, he is a son of Satan, as you would already know.) As a similar example, the Japanese translation of Gandalf the White in The Lord of the Rings is 白のガンダルフ, not 白いガンダルフ.