No, you shouldn't forget about him, even if he doesn't seem to be serious about giving his life to Jesus Christ. At present, his questions may be just a device to keep God at arm's length (so to speak), but this could change.
At the same time, I suggest you challenge your friend about his true motives. Ask him something like this: If all your questions were answered, would you then be willing to commit your life to Jesus Christ? If he's honest, he may have to say "No," because his real problem may not be his questions about the Bible. His real problem may be his will -- that is, he wants to run his own life, and he doesn't want God to tell him what to do.
If this is the case, even if you could answer all of your friend's questions he'd still refuse to give his life to Christ. And this is true of many people today. Like the rebellious citizens in one of Jesus' parables, in their hearts they say, "We don't want this man to be our king" (Luke 19:14).
Pray for your friend; God is able to do what we can't do, and He alone is able to open his heart and convict him of his need of Christ. In addition, ask God to help you be an example to him of Christ's love and peace. People may deny our words about Christ, but they can't deny the testimony of a Christ-filled life.