Do I have to re-check luggage on connecting flight?

Since both legs are on the same ticket, your bags will be checked through to Newark, and to Amsterdam on the way home. You can check with the check-in agent that this has been done, in both cases.

When you're travelling on one ticket, bags are almost always checked through. One semi-exception to this is that, if you were taking an internal flight in the US, you'd need to collect your bags at Newark to take them through US customs there. But even then, there's a special re-check counter and your bag is technically checked through; you wouldn't need to go to the main check-in area. This doesn't apply to you, since Newark is your final destination.