IPA pronunciation is
/brøː/ which means the first phoneme is b, not d.
Both are plosive sounds, but the former is formed by bringing your lips together (bilabial) while the latter has more of a bony sound because the tongue must touch the alveolar bone or the very beginning of your hard palate (alveolar, denti-alveolar).
Follow this link to hear what IPA symbols sound like.
The first thing to notice with this word is that the d at the end is not pronounced. The b is the same, but the r is pronounced like the tt in "butter" or "bottle". The ø is pronounced sort of like "uh", except your lips are protruded like a kiss. The ø is also long since there is no (apparent pronounced) consonant after it.
I can tell you're no longer active, but I hope this reaches someone else. In IPA, it is written /brøː/, or more precisely [bɾøʷː]
That's very common, yes. Especially when the syllable starting with an H is light. If the syllable starting with an H is heavy, however, the R would become very light, or disappear. Also, the N at the end of 'han' would be assimilated to the following consonant, so the pronunciation would be "Harambrø?".
No, that's not correct. It's "does he have". "Have" is here the infinitive form, while "does" is the 3rd person singular of to do. So the finite verb in English is "does" and not "have". It's the most common way to form a yes/no question in English. For 3rd person it follows the pattern: does + 3rd p. pronoun + infinitive verb.