The answers above are essentially correct in their information. The reason for the age discrepancy has to do with problems with precise dating during the 19th Dynasty - the dates float within a margin of error of about 20 years, and the exact year Ramses was born is not clear, so it's not entirely clear how old Ramses II was when he died, though the length of his reign (67 years) is fairly well established.
I believe the cause of death is usually cited as old age. Examination of his mummy would not necessarily indicate a cause of death, especially if it was from essentially natural causes. Soft tissues, such as the heart (which was left in place anyway) don't preserve terribly well or in a manner which makes it easy to analyze them to determine if, for example, he died of a heart attack. Nor would the mummified remains necessarily reveal a death by contagious disease, depending on the nature of the disease and/or the duration of the infection.
The historicty of the Exodus as related in Biblical accounts is not firmly established and what evidence there is is quite ambiguous. Traditionally, those people who accept the Biblical account as fully accurate tend to place the Exodus during the reign of Ramses II. Much of this association with Ramses II is based on the names of Egyptian cities given in the Biblical account, cities that were associated with Ramses II, though they were not necessarily founded by him in all cases, nor were they abandoned immediately after his reign. Most of these cities had very long histories, long enough for later Biblical authors to be aware of them as place-names and use those names in their account of the Exodus.
As a historical document, the Biblical texts do have their uses, but like all ancient documents, regardless of their original intent, they must be read with a critical eye if they are to be used for historical reconstruction, keeping in mind the tools scholars use to determine date of composition of texts, possible reasons behind the composition of texts, and information about the culture who composed the text and their notions of recording of information.
There is no evidence in Egypt of the sort of events related in the Exodus account, nor are their records from neighboring contemporary cultures of the events related in Exodus - a matter that would have been of much interest to some of Egypt's neighbors and rivals on the world stage at the time. Nor is their clear archaeological evidence for the Exodus or the passage into Canaan. In fact, the vast majority of cities said to have been captured in Canaan do not have evidence of destruction and capture during the broad time period during which the Exodus is likely to have taken place. There is evidence for an influx of new population groups into Canaan during this broad time period, but, again, the evidence is somewhat ambiguous and open to interpretation. Many scholars tend to regard the Exodus account as a much later creation by Israelites as a way of establishing a united history of their people and a claim to the land of Canaan. Others do not accept this conclusion, usually based on their religious faith, rather than a balanced review of the evidence, though there are exceptions. This is one of the major problems with using the Biblical texts in historical study - the Bible is still a major document in several major, living world religions and as such tends to have controversy attached to it that other ancient documents do not.