Islamic Higher Criticism of Luke

A few objections that were raised with me, copied from the infamous AC.

Who wrote Luke?

Claim:

The following is from the Catholic Encyclopedia:
http://newadvent.org/cathen/14625b.htm http://newadvent.org/cathen/14625a.htm

If Theophilus existed in either the 2nd or the 4th centuries then how could the writer of this gospel be the same Luke who is supposed to be with Jesus in the 1st century.

Did he live for 200 years?

Response:

Here, the claim is that the Gospel of Luke was written in either the 2nd or 4th century because - well, they identified two Theophilus' whom were alive in those periods. The arbitrary nature of this claim is simply laughable. How do we know it wasn't talking about Theophilus Lindsey (1723–1808)? Or some pre-Christian Theophilus? It seems that this very thorough investigative technique of typing 'Theophilus' into the New Advent search was sufficient to expose the heavly guarded secrets of the Roman Catholic Church.

Just to clarify - there is absolutely no reason to suggest that those two (of many) Theophilus' are whom the gospel of Luke was written to and for. Similarly, some reasons against the arbitrary dating would be that we physically have manuscript evidence of the Gospel of Luke dating to the 2nd half of the 2nd century (e.g. P4 & P75).