Huldah, lets cut out the rhetoric and get down to basics.
What Christadelphians Believe, is this a fair representation of what you believe? If so then Christadelphians do not accept the Bible as truth.
3. Jesus is the Son of God, and a human being, through his mother Mary. (Luke 1:30-31, John 3:18.See also God, Jesus and the Crucifixion, The Trinity)
You asked if Jesus could sin and the answer is yes He could have sinned because He was fully human and Hebrews states He had a nature like ours. However, since God was His Father Jesus did not inherit "original sin", which comes from Adam.
As to why I say Christadelphians do not accept the Bible the reasons is found here:
Colossians 1:16-23
16 For by Him (Jesus) all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities-- all things have been created by Him and for Him. 17 And He is before all things, and in Him all things hold together. 18 He is also head of the body, the church; and He is the beginning, the first-born from the dead; so that He Himself might come to have first place in everything. 19 For it was the Father's good pleasure for all the fulness to dwell in Him, 20 and through Him to reconcile all things to Himself, having made peace through the blood of His cross; through Him, I say, whether things on earth or things in heaven. 21 And although you were formerly alienated and hostile in mind, engaged in evil deeds, 22 yet He has now reconciled you in His fleshly body through death, in order to present you before Him holy and blameless and beyond reproach-- 23 if indeed you continue in the faith firmly established and steadfast, and not moved away from the hope of the gospel that you have heard, which was proclaimed in all creation under heaven, and of which I, Paul, was made a minister. NAS
Jesus was more than a human being born of Mary; Jesus preexisted Mary and according to Scripture created all that is seen and unseen.
Christadelphians, like Jehovah Witnesses deny the Trinity, which denies the fact that, the Father, Son, and Holy Spirit all have abilities and characteristics attributable to individuals.