Christianity

I get the feeling you may be working in delivery or taxi services. If someone is paying you to deliver something, as long as it is not clearly illegal/forbidden and is not UN-holy water (such as cyanide to the unsuspecting or bottles of cocaine), then just deliver their package.

Unless you are living in an area with few Christians, it seems unlikely that Christians will usually ask a Muslim to do them a favour and transport holy water to a church, as most people keep their religious practices within their own circles. But if they really want you to do this, make the best choice. I am sure they can get the idea that, as a Muslim, you aren't advocating their beliefs and are just lending a helping hand. The Prophet (S) was not hostile to Christians or churches.  

As for whether the water is holy or not after being prayed over, who knows. I would say that Muslims often treat certain items as holy - for instance, things from holy cities, tabaruk from majlis, gifts from pious individuals or scholars - even if there isn't any formal scriptural basis for this. In many countries, Muslims recite Qur'an over water and consider it to be helpful in spiritual healing. Perhaps the items are somehow blessed and perhaps they are not. The idea of blessing food and water through praying over it is found in many cultures and seems to be deeply rooted in the human psyche. There are certainly worse things to be transporting about, anyway, than water which someone has been praying over. God knows best. 

The first part of this question is really a question about the authenticity of the Qur'anic text: is it all as the Prophet Muhammad stated, or could anything have been added to it over the centuries?

Since, from the time of the Prophet, the Qur'an was heavily memorized and was transmitted by multiple transmitters, and was compiled early in Islamic history, it is unlikely that anything was added to it, as it would not have been accepted by the people. There was also a lot of strictness in copying the Qur'an. (This is in contrast to other historical manuscripts, which may easily have had interpolations) It is virtually impossible to find anyone who seriously argues that anything was added to the Qur'an after the time of the Prophet Muhammad.

For more information on the compilation of the Qur'an, you could consult Qur'anic Sciences by Abbas and Masuma Jaffer.

(From an Islamic theological perspective, the entire Qur'an is the word of God not specifically the Prophet, so technically this verse is seen as the word of God not the word of the Prophet; for the Prophet's style of speech, one could consult the hadith.)

As for Christianity itself... Certainly Christianity IS a world religion that is acknowledged as an existing religion in the Qur'an. There have been many interpretations of Christianity and ways that it is lived, and there were a number of sects in and around the Arabian Peninsula.

The Qur'an praises some aspects of Christianity and acknowledges it a religion of God, while at the same time it criticizes some beliefs or gives a different viewpoint. This is one of those differences and clearly it is a major theological difference, but it doesn't mean that Christianity as a whole has no truth or merit to it.

While the Qur'an teaches that all prophets before the time of Islam, including Jesus, taught the same message, it does not say that every religion that emerged was absolutely correct or identical. Even just considering Judaism, Christianity, and Islam, there are obviously major differences between them! Rather, the position of the Qur'an is that some people deviated from the teachings of their prophets or introduced incorrect beliefs or practices, and this is why there is variance in religions.