Or at least do people who believe that there's a connection between race & intelligence believe that a person's race would determine what kinds of topics a person would be interested in?
No - that would be illogical. We are all a mixture. Nobody is one race anyway, so any differences you can see, such as skin colour, have a very small effect on who the person is.
First of all, you should read The Race Myth by Joseph Graves, as he illustrates the fact that there is no such thing as "race". Secondly, he describes in detail what you just touched upon regarding the connection between race and intelligence -- which DOES NOT exist at all. He discusses IQ tests, which have historically been catered to one population or demographic, and also talks about the origins of race in America.
Basically, you need to completely eliminate the idea of race as a biological categorization from which you can determine culturally distinct traits and/or predispositions. Turns out, the two most "racially distinct" individuals living today only differ by .1% of their DNA, and even still, the vast majority differ by much, much less. You cannot determine a person's "race" through genetics, despite the effort that has been made in the past to prove that you can.
Short answer - Absolutely not, race has nothing to do with an individuals intelligence, cultural interests, or mental capacity.
I think that you are confusing race with ethnicity. Yes, someone of a certain ethnicity may be predisposed towards the values of their social group. Biological race? Nah!
Culture is a far greater influence than what you look like.
I grew up in a heavily multilingual environment and my parents are multilingual as well. Ever since I was a kid, all I wanted to do was learn everybody's language in the neighborhood (Fukien next door, mandarin down the block, Japanese across the street, Italian from that guy in the market...)