Mohamed, a True Prophet?

I want to share some questions I asked in a discussion I had recently with a Muslim:

Was Mohamed a true prophet of Allah?

Can a true prophet of Allah, when speaking as a prophet, lie?

Did Mohamed, speaking as a prophet, say that Jesus was a prophet?

Did Mohamed, speaking as a prophet, say that there is only one God and He cannot have a son?

Did Jesus claim to be the Son of God?

(Matthew 27:43 “for he said, I am the Son of God.” Luke 22:70 “Then said they all, Art thou then the Son of God? And he said unto them, Ye say that I am.” John 3:18 “He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.” John 9: 35 “Jesus heard that they had cast him out; and when he had found him, he said unto him, Dost thou believe on the Son of God?” John 10 36 “Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God?” John 11:4 “When Jesus heard that, he said, This sickness is not unto death, but for the glory of God, that the Son of God might be glorified thereby.”)

Was Jesus telling the truth or was He lying?

If Jesus was telling the truth then He is the Son of God. If Jesus is the Son of God then Mohamed lied when he said, God cannot have a son. And if Mohamed lied then He can not be a true prophet of Allah.

If, on the other hand, Jesus is not the Son of God then He lied when He claimed He was. If Jesus lied about being the Son of God then He is certainly not a true prophet. And if Jesus is not a true prophet then Mohamed lied when he said that Jesus was a prophet. If Mohamed lied about Jesus being a prophet then Mohamed cannot be a true prophet of Allah.

Is it true that whether Jesus is the Son of God or not Mohamed is a false prophet?

Now tell me, doth this offend you?