I did give my understanding of these verses on another thread, but it really is no good saying that Christ learned obedience as we might, since He was already obedient. I think you need to explain exactly what you understand by the term.
As I have also written before, punishment (or chastisement if you prefer) can be either remedial or retributive. I pointed out Amos 4:6-12, where remedial punishment unheeded leads to a final retributive punishment.
However, to move on, there are two aspects of the work of a High Priest. The first, as illustrated in Hebrews 4:14 - 5:11 deals with our Lord's work as an intercessor. The second, found in Hebrews 9:1 - 10:18, covers His sacrificial role. He alone has offered the one, perfect, acceptable sacrifice for sin (Hebrews 9:12-15), '......and for this reason He is the mediator of the new covenant, by means of death, for the redemption of the transgressions under the first covenant that those who are called may receive the promise of eternal life,' and this leads into the wonderful promise of the new covenant in Hebrews 10:15-18. It is because Christ has paid for those sins, that there is now no longer any need for a sacrifice for sins (v.18). All this in sweet accord with Romans 3:23-26. Moreover, 'Do we then make void the law through faith? Certainly not! On the contrary, we establish the law' (Romans 3:31). The law is established, honoured, fulfilled by Christ suffering in the place of sinners, so that God can be just and the justifier of the one who has faith in Jesus.