Can proteins move outside cells?
Yes. All proteins actually begin to get synthesized on cytoplasmic ribosomes but if they are going to be used for extracellular purposes, they are tagged and whole ribosome is taken to ER where protein synthesis is completed. The proteins are exocytosed with help of Golgi body, the post office tagging and packaging organelle (the Golgi body packages these proteins into the vesicles that fuse with the plasma membrane).

Examples of this process are: the pancreas secreting insulin for blood sugar control, digestive enzymes for digestion, the immune system telling the body there's a bacterium we must fight it and calls more immune cells (cytokines). Most proteins of course stay in the cell, and are necessary to make the cell or carry out metabolism or DNA transcription.