Your other points are correct (Muslims believe the Lord Jesus Christ was a prophet, and was virgin born of Mary), however - as I understand it - they do not believe He was crucified, died, was buried, and rose the third day. They profess to believe the Gospels - but yet they deny the Scriptures.
They claim 'someone' took the Lord's place at Calvary (e.g., Barabbas, Simon of Cyrene, Judas, etc) - and God just 'beamed' the Lord Jesus up to Heaven.
Peter Hammond has a good audio series on Islam - if you care to spend a couple of hours listening to his material. I thought it was pretty instructive.
Muslim Evangelism Workshop - Peter Hammond
The bottom two talks: Comparing the Quran with the Bible, and Understand the Challenge of Islam, were pretty good.
bkmk