Can the same Pokemon have a different max CP in Pokemon Go?

If you and your friend are the same player level, no. Max CP is based solely on player level and type of Pokemon. Each Pokemon has the same max CP at the same player level. If you max out 2 Pidgeys they will have the same CP. As Joe pointed out there can be a difference in HP. I'm fairly sure this is based on size and weight (XL vs XS), but those minuscule amounts of health don't amount to much in a gym battle.

The stats will definitely differ for different instances of the same pokemon. For example, I have 2 Fearows, one is 338CP and has 50HP, the second is at 358CP and has 48HP.

I believe that max CP is related to your trainer level as well, so the higher level you are, the stronger your pokemon can become.

Yes. Though I don't know all the details, player level seems to have effect on this (so I've read), but it also depends on the individual pokémon. To illustrate, these screenshots are from the same moment, yet you can see that the CP bars are filled differently, thus showing different max CP stats. Whereas for the first magikarp 10CP is about 25%, for the second magikarp it's significantly less (although I don't know from what percentage the bar does in fact fill).