i can't answer your first question about how many semitic languages there are, but i can talk about about some of your other concerns.
first, there is a the problem with thinking that hausa is semitic. semitic is a group of languages that includes Arabic, Hebrew, Maltese. hausa is only a language, not a group of languages. hausa belongs in the chadic group of languages along with bole, ron, angas and some other languages.
afro-asiatic is the larger group that includes semitic and chadic. arabic is in the semitic subdivision of afro-asiatic, and hausa is in the chadic subdivision of afro-asiastic. so 'semitic' and 'hausa' are not at the same level of classification.
hausa and arabic are related language because they are both afro-asiatic. think of them as distant cousins rather than brothers. arabic is a brother of maltese because they have the same parent, and hausa is a brother of bole because they have the same parent. but the parents of arabic and hausa are different. the parents have the same grandparents perhaps, or great-grandparents.
what all this means is that hausa is not semitic. for a better idea of the classification, see http://www.ethnologue.com/show_family.asp?subid=52-16.
unfortunately, i'm not an expert in these languages, so i can't speak to the validity of the classification system that places arabic as a semitic language and hausa as a chadic language into the same afro-asiatic family. i suspect that it is placed on greenberg and i have many reservations about greenberg's classification schemes, but that's another discussion.
now, about the hausa people. the hausa people are those people whose first language and whose heritage is hausa. however, hausa is spoken by many people as a second language. these people are not hausa. so not all hausa-speakers are hausa, just as not arabic-speaking people are arabs or english-speakers are english.
unfortunately, we often use the name of the language to refer to the people who speak that language. so we call the hausa people 'hausa' because they speak the hausa language. for the same reason, people often refer to speakers of semitic languages as 'semitic people.' this sometimes makes the discussion very confusing, especially if people confuse 'semitic' and 'afro-asiatic' and 'islamic.' this hides the differences among the peoples who are all labelled the same way.
finally, the hausa are not a 'race' of people. 'race' means that a group of people are genetically distinct from other peoples. sometimes the word 'race' is confused in non-academic speech with 'ethnic group' or 'cultural group,' and i think this is how you are using the word. yes, the hausa people are an ethnic group of their own, distinct from other ethnic groups in the region like the fulani or tuareg. they have their own history, their own genealogy, their own traditions. although they are now islamic and share this aspect of their culture with their neighbours, still they are ethnically and linguistically their own people. but they are not a race of peoples.
hope this helps!