Is there ever a perfect pause to join a conversation?
No. Go ahead and join, just try not to interrupt to much.
Is going up to someone or a group you don't know and saying hi and your name a great strategy for making friends? Why or why not?
No. It is awkward as a teenager to do that. People may think you are strange.
Name a type of prop you could use when starting or joining a conversation.
Phone, book, journal etc.