Is going up to someone or a group you don't know and saying hi and your name a great strategy for making friends?
No. It is awkward as a teenager to do that. People may think you are strange.
Should you share a common interest when starting or joining a conversation?
Yes! It gives you something to talk about.
What does it mean to check someone's interest when starting and joining conversations?
Are they talking to me and facing me? Is the group circle open or closed?