"I do not want a purple skirt."
"i" & "no" particles are added to turn noun into adjectives. 5 primary color (Red, Blue, Yellow, White, Black) are "i" adjectives. Red - Aka (noun), Aka"i" ("i" adjective) - Akai kuruma (Red car). Other colors are "no" adjectives. Purple - Murasaki (noun), Murasaki"no" ("no" adjective). Murasaki no kuruma (Purple car), Murasaki iro no kuruma (Purple colored car).
Interesting, it only wants the の if you use むらさきいろ not just with むらさき. I thought these were equivalent, is there something I'm missing?
むらさき is still a noun. It can mean the purple color, but also mean a type of flower (gromwell), so it is more common to refer the color to むらさきいろ.
The negated form of i-adjectives removes the final い and appends くない.
In polite Japanese you can also use くありません instead of くないです, but I've read that くないです sounds more natural in everyday speech.
Could this be を instead of は? Or are we able to skip using は altogether to turn the sentence in casual form? (I didn't have a は and it was incorrect)
IIRC, ほしい is an adjective, not a verb, so you can't use を, which marks objects of a verb. You can however use が instead, which can be used to mark objects of an adjective.
You can skip most particles for casual speech, it's what most native/fluent speakers end up doing.
This is a good question that learners like me struggle with. To a non-Japanese speaker, it seems there are a few words that are generally preceded by が where you might otherwise expect は, most commonly "feeling" adjectives like ほしい and 好きい. Sometimes, in negative sentences like this, they're preceded by は. It's not a rule, and I don't know why it happens, but of course nobody seems to have a decent explanation.
Right, you have a good point. I can tell, when a person is fluent enough, he will not be able to tell easily why a grammatical feature is written or spoken like that quite a lot of times. This is the case of は and が where one can only grasp the difference in each scenario when he is very fluent.
The basic idea is this graph - when you have to choose one from a number of choices in the former part of the sentence, use が, and if the choices are in the latter part, use は
You have fixed your topic as スカート. You have two choices ほしい or ほしくない. So スカートはほしくない.
You can say スカートがほしくない, when you have a number of choices スカート, ワンピース, ブラウス and the one you do not want is スカート.
There is really not an obligation to use が with ほしい, いい, 好き, 嫌い, できる, or the potential form.
Why is ほしい in this sentence considered an adjective? 'To want' is a verb, as is 'I want'. Therefore, should the verb form of ほしい not be used?
It is because "to want" is commonly used as an adjective ほしい or 〜たい in Japanese. It is a difference between two languages so please just accept it. 欲（ほっ）する is the verb but it is not very commonly used.
It would seem that in japanese, many things that would be considered with a subject/verb/object construct in other languages, are instead dealt with using a "property of being the subject of a particular verb" instead. This property belongs to the object rather than being done by the subject and is thus more like an adjective. Objects have the property of being liked or being wanted (by me) for example.
Think of words like "want", "like", "need", and "hate" to be the adjective participles "wanted", "liked/preferred", "necessary", and "hated".
shouldn't it be "na" instead?? was always taught that non -i adjectives get a 'na' between them and the noun. like "orenji na kutsu"
No, always use の for connecting two nouns. If it is a な-adjective （the formal name is 形容動詞 けいようどうし）, then connect using a な. A proper dictionary can tell you whether a word is a noun or a な-adjective.