It does sorta look like beech. Looks sorta too dull too to be beech. Looks almost like elm, but I don't think it's elm either. I'm going to drag out some of my very dry elm and take an end grain look at it.
As far as the oil: FDA likes mineral oil a lot. We make cutting boards commercially here, and all we use is mineral oil. Since you have end gran there to cut on, I see no reason why you'd ever want to flip the board over, so I'd also put rubber feet on the bottom just to make sure water doesn't get into that end grain. That's a good looking board you have there.
As far as the oil: FDA likes mineral oil a lot. We make cutting boards commercially here, and all we use is mineral oil. Since you have end gran there to cut on, I see no reason why you'd ever want to flip the board over, so I'd also put rubber feet on the bottom just to make sure water doesn't get into that end grain. That's a good looking board you have there.