'ha' is part of the infinitive tense 'å ha', which is used after a modal verb such as 'kan', 'vil', 'må', etc...
'har' is the present tense.
How do I say "Can I have an orange dress?" - Kan jeg ha en oransje kjole, takk?" Just curious...
I think your sentence can be used but it may depend upon the intention of your question. By this I mean if you are asking 'Am I allowed to have an orange dress?' or 'Do I have the option of having an orange dress?' I think your sentence may work with my first sentence whereas, I think the second would be 'Kan jeg få en oransje kjole'.
I am learning norsk so I may be way off with my suggestion and understanding but hopefully it may point you in the right direction to satisfy your curiosity.
Why is it "one orange dress" and not "a orange dress" ? I'm a bit confused how you would otherwise say "a orange dress" ...
"an orange dress" would have been accepted.
You use the indefinite article "a" before nouns that begin with a consonant sound, and "an" before nouns that begin with a vowel sound.