Aren't there tenets in Christianity or is the simple belief in God means you're saved, regardless of your actions? Wouldn't God love those who do what he ordered them and avoid what he forbade them?
Paradise and salvation are rewards we have to obtain by following God's orders. Being a reward, we MUST prove we deserve it by doing works God told us to do and for us to seek his salvation and mercy with our deeds and belief.
1 - Yes, Jesus (PBUH) is a prophet of God and one of the 5 main messengers of Allah, the others being Noah (PBUH), Abraham (PBUH), Moses (PBUH) and Muhammad (PBUH). He's hold in very high esteem and is considered the Messiah of end times. The teachings of Islam are in line with Jesus' message of strict monotheism and submission to God.
2 - Christianity has been corrupted and I don't see how Jesus (PBUH) would've declared himself as God's son, rather than being his prophet. Allah/God has no daughters, what you reffered to was Arab Jahiliya (age of ignorance) paganist beliefs
3 - Muhammad (PBUH) prophecies can be found in the hadiths and his sayings.
http://www.iqra.net/Hadith/prophecy.php
And the Quran sent by God to his messenger is his ultimate miracle