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the friction of the skateboard is rolling because the skateboard has wheels and static because the person is standing on the skateboard.
Both are static, both between the wheels and ground as well as the foot and the grip tape: The wheels are not skidding; in essence, they are rotating, yet not moving, so the frictional force would be the -(coefficient of static friction*mass*acceleration due to gravity), negative because it is opposing the direction of the applied force (pushing) or momentum. OP was right on the person standing, unless you are readjusting your feet constantly, that would be static, even thought standing without movement of your feet has no friction because there's no horizontal force exerted along / into the skateboard by the feet (other then Force due to gravity, but that's straight down and doesn't effect gravity in this case.)
Friction effects both the contact between the wheels and the ground, as well as your shoe and the grip tape. You would like a high coefficient of static friction between the ground and your wheels so you don't end up skidding, fishtailing, and later flat-out falling down. Also, you would want a medium-level coefficient of kinetic friction and possible a medium-high coefficient of static friction between the grip tape and your shoe in order to grip the board, yet still be able to slide your foot for flip tricks. If the coefficient of static friction between the grip tape and your board is too high, it won't flip properly as it might overflip or flip on an unusual axis if it were to be too low. As you use the grip tape, both coefficients will decrease because the grains on the grip tape will be smaller and easier to pass over with a lesser repelling force of friction.
Coming from a skateboarder in college-level physics.
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What forces are acting on a moving skateboard?
The main forces acting on a moving skateboard are friction with the ground, air resistance, and the force applied by the skater to propel the skateboard forward. Additionally, there may be gravitational forces affecting the vertical motion of the skateboard.
What are the forces act on a skateboard?
The main forces acting on a skateboard are gravitational force pulling it downward, normal force exerted by the ground upward, frictional force opposing its motion, and air resistance when moving. Additionally, the skater applies a force to propel the skateboard forward and can use their body to maneuver and balance it.
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This is a mighty vague question, but I'll give it a shoot. A skateboard has wheels - when these wheels are acted upon by a force (such as you pushing it), they proceed to take the energy from that force and change it into centrifugal and centripetal forces- this causes the wheels on your skateboard to turn. Your skateboard won't roll indefinitely from 1 push because while your skateboard is rolling it is creating friction with the sidewalk you're skateboarding on. Friction is caused when 2 objects rub up against each other - this creates heat and a transfer of kinetic energy. Once all the kinetic energy has been transferred from your skateboard's wheels to the sidewalk, your skateboard come to a stop.
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