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.
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.
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