Sanding or cutting off these bits will make assembly easier. Remember to cut away from yourself and preferably towards some sort of cutting board. Before glueing any pieces clean all surfaces and check for fit. All paint should be removed from contacting surfaces. Also, be careful not to damage any painting you have done.
Different glues are available for different needs.
Tube cements weld the plastic together in a permanent bond. Used sparingly, tube cement is very effective. Liquid cement is applied while holding the parts together. The entire seam is fused by allowing the liquid cement to run along the joint. Crazy glues are also a possible option.