In My Area: Possessive Statements in Hindi

So I'm just about to get started on a study of "quirky" case marking in Hindi (supposedly subjective arguments that are marked as datives). I'm pretty excited about it because it's Hindi and it's syntactic. My Hindi knowledge isn't deep enough yet to make any thorough arguments but I do have initial impressions based on my knowledge of possessive forms in Hindi.

There is no verb in Hindi for "to have." There are plenty of verbs denoting movement of a possession - you can get, take, bring, drop, whatever - but no verb peculiar to the act of possessing. For things that in English are had, there are a couple different constructions:

For something possessable/alienable, you essentially say that one of those things is in your area:
मेरे पास किताब है|
Mere paas kitaab hai
My.pl nearby book is
"I have a book."

For something inalienable - a relative, a body part - you say that one of those things is yours:
मेरा एक बंधू है|
Mera ek bandhu hai
My.mSg one brother is
"I have one brother."

The having of diseases is put into an experiential pattern, which brings us to the issue of potentially subjective datives:
मुझे बुखार है
Mujhe bukhaar hai
I.Dat fever is
"I have a fever."

My initial reaction to the idea that "Mujhe" is the subject in this last sentence was skeptical. Surely, as the verb is taking the third-person form, the subject must be the third-person "bukhaar," or else the verb would be "huun". Arguments have been made that dative subjects do not have to affect verb forms - an apparently substantiated claim on which I reserve my judgment for the moment. On the other hand, Hindi does occasionally allow subjects to be dropped and I believe the following possible sentence may be grammatically worth considering:

बुखार है
Bukhaar hai
fever is
"I have a fever."

More to come on this phenomenon and probably lots of other Hindi goodies. For now, नमस्ते