Are you referring to the jizya? If so, 9:29 is clearly describing a scenario in which fighting and subjugating is indeed happening where you are, therefore the ruling Islamic authorities would be the tax collectors. How is that not the bleedin' obvious?
No, Christians are NOT believers.
5:68 - "Say [to them, Mohamed], "O People of the Scripture, you are standing on nothing until you uphold the Torah, the Gospel, and what has been revealed [the Qur'an] to you from your Lord."
5:72 - "They have certainly disbelieved who say, "Allah is the Messiah, the son of Mary."
19:88-91 - "And they say, 'The All-merciful has taken unto Himself a son.' You have indeed advanced something hideous! Whereby the heavens are almost torn, and the earth is split asunder, and the mountains fall in ruins, That they ascribe a son (or offspring or children) to the Most Beneficent."
Read that last one as many times as it takes for Islam's revulsion of Christian belief to sink in.