Andy - yes, there is indeed evidence and references to the points raised, as well as Christian arguments why they disagree with the similarities pointed out.
Mithra was indeed a 'sun god'. Krishna in Hindu literature and his story is well documented.
For example, here is a website I found after a quick search which has references for the points it makes about Mithra:http://www.truthbeknown.com/mithra.htm
Indeed, the date of December 25th for Christmas - birth of Jesus - was a date chosen in the 'Western Christian' church around 300 CE and is not based on the Bible at all. Jehova's witnesses don't follow this date, and the Eastern Orthodox Christians have a different date (Jan 6). In pre-Christian times, Dec 25 was a Roman pagan festival of the birth of 'Sol invictus'.
Helios in Greek mythology is the 'sun god' and is depicted in drawings and sculptures with a 'halo' - rays of light around his head:
The similarities of the depictions of Jesus with a Halo are striking.