Regarding the question of who the author of the last verses of the Torah is, there is no contradiction between the fact that the Torah speaks about Moshe in the third person and the assumption that Moshe wrote the Torah.
Among the medieval commentators there are two different approaches concerning the verses that appear to have been added at a later time. The more widely accepted approach attributes them to Moshe, who wrote them in a spirit of prophetic foresight. The other approach, advocated by Ibn Ezra and some of the sages of Germany, maintained that the Torah contains verses that were added by prophets at a later stage.
The approach of Ibn Ezra and The German sages was based, of course, on the ancient tradition of the Book of the Torah having been written by Moshe at God's command, with a willingness in principle to recognize the occasional later addition. Spinoza, who essentially was the father of modern Biblical criticism, claimed that the phenomenon of later additions in the biblical text is not a matter of a few isolated examples, but rather indicative of a much broader body of later writing that ultimately concludes that the entire Torah is a composition dating to a time later than Moshe.
Yet an objective appraisal of the discussed verses seems to indicate the very opposite: they may certainly be deleted with ease from the text, and they are not integral to the narrative itself. Therefore, there is no reason not to adhere to the path set by the medieval sages, and to view these verses as exceptions which indicate nothing about the origins of the text as a whole.
The Torah cannot be Moshe's own autobiographical book, since parts of it describe events that preceded his own birth, while other parts describe events of which Moshe could not have had any knowledge. The Torah is not Moshe's personal book, narrating the events of his life and his actions; its importance is derived specifically from the assumption that it expresses God's word. There is therefore no contradiction between the fact that the Torah speaks about Moshe in the third person, and the assumption that Moshe wrote the Torah.
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Edited by the HaTanakh Site team