1. get plastic caps locally and install. no, air will not leak out when you remove the cap.
2. you can use a screw driver from the back to push out the tabs gently. no science to center caps. you will need to remove the wheel from the car to do this.
3. stock lugs are for hubcentic wheels. your wheels are lug-centric by design. look at them and compare. they will not work.
have a safe trip back.