That's one way of looking at rights that was popular in the 18th Century. Another way to look at rights would be duties and obligations. And then there's the argument as to whether "natural rights" exist extrinsic to man and man made rights were are sometimes called legal or legislative rights. Jeremy Bentham for example didn't believe in natural rights. Generally(but not exclusively) natural rights and natural law are associated with religious thinkers and the concept dates back to Aquinas and earlier.
Of course not! You think I want to have to eat around a bunch of niggers? No but seriously, the problem with many libertarians is they take a maximalist, extreme position on negative rights. You can see how loopie it is when they have to actually articulate a working system. Just take a look at the crackpot stuff that Rothbard and more recent kooks like Molyneux have come up with. They're cranks and shouldn't be taken seriously.
We should of course lean towards giving businesses, private individuals and entities as much freedom as possible to conduct lawful business or other activities however they see fit. The particulars of the whole range of anti-discrimination and post 60's "civil rights" legislation, particularly in the form of positive rights as you mention is a major problem of course. But I don't think it's in anyone's interest to concentrate on the aspects of civil rights legislation pertaining to forcing businesses to serve everyone. There are more important things to tackle.
I believe in natural rights. Aquinas, Hobbes, Locke and others have described very similar definitions of natural rights and they pretty much accord with mine; in a nutshell, a right to life, liberty and private property.