Well, the line about Pike being "about" Kirk's age probably wasn't thought too hard about at the time. I believe the writers were thinking more about Jeffry Hunter at the time. I suppose, 10 or 15 years older isn't that much. I think Mendez was trying to put emphasis on the tragedy of the situation by both comparing Kirk and Pike together (showing how similar they are) and how much more life Pike had ahead of him. Truth is, that by the time Mendez was talking about him, he wasn't handsome or active anymore.
It's never really stated whether or not the 3 years we see out of Enterprise's 5 are the beginning, middle or end of the mission. It could also jump around a little.
One could also assume that Enterpise underwent a refit before Kirk took command and then again while under his command. As the ship looks different both inside and out between "The Cage," WNMHGB and the rest of the Trek series.
The fact is, that Tyler never mentions warp drive when he says "the time barrier." It seems likely that this was what they had in mind when writing it, but it's never specifically stated. It wouldn't make any sense if it had been warp drive... as it would have taken centuries to reach other star systems without it. Current theory is that it was some sort of barrier in warp speed that limited how fast they could go... all be it, still at warp.
I'm still trying to understand why the Enterprise is said to be 20 years old in Star Trek III...