What type of wood are the cabinets? I have heard that the grain shows through when you paint oak cabinets and I can't tell from the the picture.

I’m certain a cabinet maker such as Woodmode would not paint a grainy wood such as oak. I’m sure they’d select Maple or some other smooth grained species. Checkout Woodmode’s website—I’m sure they specify options for painted cabinetry. Of course, many people who want to renovate will paint or attempt to paint all types of cabinetry in hopes of achieving a refreshed look. Sometimes the result is great, other times not so great.