Does this dress fit nice? 'nicely' Does this dress fit good? 'well' not 'good' How does this dress fit? 'fit me' not 'fit' How does the dress fit? OK, if you are asking someone else. How does this dress look on me?OK

Definitely use the demonstrative/identifier "THIS" instead of "THE", especially if the speaker is wearing or holding the clothing. I like the option you gave with the phrasal verb "look on": "How does this dress look on me?" Remember that if you use "fit", the proper qualifier is an adverb such as "nicely" or "well" instead of "nice" or "good"

In principle, these little phrases which are not used in English. :-+

I think the options Does this dress fit nice? How does this dress look on me? Would be appropriate.