You have to LISTEN carefully. When they say ''If this is a pen, is this a pen", say yes. When they say "Is this a pen?", say no. Then they are going to ask, "But if this is a pen is this a pen?",...
"I have a pen" is correct. "I have my pen" would also work. "my" shows ownership as does "I". But this is one of those things....like why certain words are masculine in Spanish. It just Is.