I'll be traveling to Luxembourg, I have a flight from a small airport in Moline USA which my checking in and carry on bag is scanned in, I will be going to Chicago then to Frankfurt (first Schengen Area) before flying into Luxembourg, will I need to go through security check point to check in my carry on bag after going through passport control?

If you stay airside between flights, probably not.

If your flights are all on one ticket your bag can be checked at Moline through to Luxembourg, which is a Schengen country. If your FRA-Luxembourg flight is on a separate ticket you can ask for your bag to be checked through but it may or may not be possible (do have your FRA-Luxembourg ticket handy at Moline check in.) If you cannot check your bag though from Moline, you will need to retrieve your bag after clearing passport control in FRA and then recheck it with your new airline in FRA.

For your carry on, you may need to go through security after clearing passport control depending on whether you can stay airside for your connection.

You may know this, but Frankfort is a huge airport and we had to grab our luggage and go through customs before connecting to Salzburg. We started at O'Hare in Chicago. We were told our luggage was going straight through, but were told on the flight that everyone needed to pick-up their luggage at the baggage claim. In addition, waiting at the gate, the plane was on the tarmac and we needed to take two flights of stairs with all our carryon luggage to get on a bus for a 7 minute ride to the plane, that was broken and we had turn-around and go back to the gate, up the two flights of stairs and wait until they had another plane and repeat the process. The elevator was out of service. We will do whatever we can to avoid Frankfort, we had that bad of an experience.