Queer I quickly perused over one of the sites you mentioned. It has a link to a Christian Mission homepage, which should tell you something about the contents. In my opinion, the best way to understand Islam is to ask a Muslim, as the best way to understand Christianity is through a Christian. The page is full of truths and what Muslims would consider half truths. So I guess it depends on whose truth your looking for.
In terms of Christianity - what exactly do you mean by "connection with Islam"? Islam teaches that Jesus was a Prophet of Allah. Jesus recieved the same message as Muhammad, as did Moses and Abraham. The message was misconstrued and corrupted over the ages. Jesus is exalted in position in Islam and holds a special place in the hearts of Muslims:
"Say (O Muslims): We believe in Allah and that which is revealed unto us and that which was revealed unto Abraham, and Ishmael, and Isaac, and Jacob, and the tribes, and that which Moses and Jesus received, and that which the prophets received from their Lord. We make no distinction between any of them, and unto Him we have surrendered." (QS. 2:136)
An entire chapter of the Qur'an (chapter 19) is named after Maryam (Virgin Mary). In Islam Christians and Jews are considered "People of the Book". They are distinct from other non-Muslims. Although they are believed to have corrupted and misconstrued Allah's message, they are respected and permitted to enter heaven if they are righteous in their deeds:
"Lo! Those who believe (in that which is revealed unto thee, Muhammad), and those who are Jews, and Christians, and Sabaeans - whoever believeth in Allah and the Last Day and doeth right - surely their reward is with their Lord, and there shall no fear come upon them neither shall they grieve." (QS. 2:62)
In Islam, Jesus is not believed to be crucified. In Islam, Jesus did not die. He was "ascended" to heavan and will return:
"(And remember) when Allah said: O Jesus! Lo! I am gathering thee and causing thee to ascend unto Me, and am cleansing thee of those who disbelieve and am setting those who follow thee above those who disbelieve until the Day of Resurrection. Then unto Me ye will (all) return, and I shall judge between you as to that wherein ye used to differ." (QS. 3:55)
"And because of their saying: We slew the Messiah, Jesus son of Mary, Allah's messenger - they slew him not nor crucified him, but it appeared so unto them; and lo! those who disagree concerning it are in doubt thereof; they have no knowledge thereof save pursuit of a conjecture; they slew him not for certain." (QS. 4:157)
I hope that answers some of your questions. The question of Jesus and his teachings in Islam is very complex and could occupy volumes of books.
Achtung ;)
"O People of the Scripture! Do not exaggerate in your religion nor utter aught concerning Allah save the truth. The Messiah, Jesus son of Mary, was only a messenger of Allah, and His word which He conveyed unto Mary, and a spirit from Him. So believe in Allah and His messengers, and say not "Three" - Cease! (it is) better for you! - Allah is only One God. Far is it removed from His Transcendent Majesty that He should have a son. His is all that is in the heavens and all that is in the earth. And Allah is sufficient as Defender." (QS. 4:171)