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If I want to say:
1) I have a bag - у меня есть сумка
2) I need this bag - мне нужна эта сумка
(Why I can't say я нужна эта сумка and I need "мне"?)
3) I want this bag - я хочу эту сумку
(Why is not я хочу эта сумка? and why if I use scarf and not bag I need to use этот? Like я хочу этот шарф )
2. Because this is how Russian works.
The need of a speaker in Russian is normally expressed indirectly through Dative case
мне требуется / необходима
This is likely because someone's need is perceived in Russian not as an act or volition, but as a state. Unlike at least in English the actor here is not the person who needs but the object which is needed.
That's why in the sentence Мне нужна эта сумка the subject is эта сумка. It's as if the bag were acting upon yourself making you need it.
It's possible to say я нуждаюсь в этой сумке but the verb нуждаться is a little stronger than to need, it means that you can't do without it or that you pine for it, which is a volition.
3. The verb хотеть governs Accusative case for inanimate objects, therefore сумка assumes the form of сумку as expected of it in Accusative.
3A. Шарф is a masculine noun inflected in Accusative, the masculine demonstrative pronoun этот must agree with it in grammatical case, hence этот, which is its form in both Nominative and Accusative cases.
Cумка (cумку in Accusative) on the other hand is a feminine noun therefore it requires feminine demonstrative pronoun эта whose inflected form in Accusative case is эту.
