One of the reasons Jesus came was to show us something about God. In this instance I think to question who said what, when and why etc. can muddy the water. God wanted us to know him through Jesus, and the bible is the only means we have to do this. I must presume God knew this.
So when we look at him what do we see, what does he say? He shows he cares about everyone, the poor, women, the sinner, children. One of his prime motivations is freedom for all. He wants people set free from whatever holds them in chains. He came to tell us about the kingdom, that we are no longer orphans. All can be ours if we want it.
He was fully human, fully God. We don't really understand how that works, but when he healed and did his miracles he did them as a human. Why? To show that we could do them too. If he did them as God they would be beyond us mere mortals. He sent the disciples out to also show that this was something for us to do and encouraged with the words that we were to do what we had seen him doing and more.
Did he know what the future for medicine would be. Probably not, but I am not sure if this is relevant to his healing people. After all some people 1,000 (a rough number) of years before were far in advance of us in some areas. That wasn't relevant either. But I do believe that he knew about each persons needs and tailored what he said and did for each. How did he do this as a human? Well I think he tells us and it is also a guide for us. He said he only did what his Father told him and he did what he saw his Father do. He listened to his Father's voice and was guided by him. The Father knows exactly what the problem is and how best to help set the person free. Of course Jesus being Jesus had a crystal clear connection to the Father except for that one time on the cross when sin got in the way. When Jesus left he sent us Holy Spirit and a way to have a Father child relationship with God too. Holy Spirit is to teach us all truth and remind us of all Jesus said. Holy Spirit has the gifts which he gives to us, and Jesus left us with the authority to go out and do these things in his name. So he demonstrated the blue print, showed us God's will. Gave us the authority, and the power and the guidance of Holy Spirit to listen to. Then told us to go and get on with it, as we are his hands and feet. We continue to set the people free in his name.
