No, it isn't hopeless to share your faith with anyone, even someone who asks questions you can't answer. Humanly speaking, no one was a less likely candidate to become a Christian than Saul of Tarsus. But God intervened and he met Christ, and Saul the persecutor became Paul the preacher (see Acts 9:1-19).
And that is the key: Only God can convict someone of their sins and their need of Christ, and only He can bring them to Himself. Jesus said, "No one can come to me unless the Father who sent me draws him" (John 6:44). Does that mean our witness isn't important? No, of course not. But God is able to take our witness and use it - even when it seems impossible.
Often, however, people who put up one objection after another aren't really interested in getting answers - and this may be the case with your friend. The real problem is their will; they simply don't want to yield themselves to Christ and have Him take control of their lives. Paul answered every question the Roman governor Felix had for him - but finally, the Bible says, "Felix was afraid and said, 'That's enough for now! ... When I find it convenient, I will send for you'" (Acts 24:25). But he never did.
Pray for your friend, and ask God to help you witness to Him - both by your words and your life. You may not be able to answer all his questions - but the greatest answer is your life.