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
.