¿Can you believe in an old earth and a global flood?

In general Young Earth Creationists believe in a global flood firstly because they adhere to a simple, literal reading of Genesis (which is why they believe that the Earth is young in the first place) and because it's the least bad explanation for the fossil record they can find.Old Earth Creationists are more inclined to looser readings and tend to have a greater respect for the physical evidence (which is why they accept that the Earth is old). A local flood is not ruled out by Genesis and fits better with the actual evidence.I would guess that your friend adheres to one of the ideas which tries to fit an Old Earth with a fairly strict reading of Genesis such as "Gap Theory". "Gap Theory" postulates a long gap between Genesis 1:1 and 1:2 with the world created in 1:1 laid waste at the end of the period (leading into 1:2).

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Genesis 1 simply states that when they were created God did it. The determination of the 24 hour day was not established until day four when the sun and moon were created according to the literacy of the record.

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That's not a strict literal reading at all. The day/night cycle is established right at the start - Genesis 1:3-5. There are evenings and mornings before the 4th day (e.g. Genesis 1:5). There's no indication of any change to the timing of that cycle from that point on.Saying that there was some large unspecified amount of time before Genesis 1:3 is not literal either. It's not in the text. A strict literal reading is not going to assume that without a good reason.