Why was the crucifixion necessary ?

[Undeceived]

I believe so. Any execution would have worked--the point is that Jesus had to be sentenced and die for a crime he did not commit.

Why ?

Because 'justice' is not served. Jesus is punished for sins he did not commit (namely, ours), while we go unpunished for sins we did commit. They cancel out nicely, don't you think?
Could this have been accomplished by natural death? That is not ruled out, because the Bible does not rule it out. An execution is stronger thematically. It mirrors our own situation. That's as far as I can go.

Explain exactly how god/jesus dying redeems us ?

We break the inherent law of goodness in nature. We deserve punishment (the way a murderer does). Jesus takes our place. Thus, we do not have to die. And God can remain perfectly just (since letting us go scot free he would be unjust). But God/Jesus is more powerful than death, as Acts 2:24 says, "But God raised him from the dead, freeing him from the agony of death, because it was impossible for death to keep its hold on him."
Jesus' new life gives us hope that we will resurrect also.

If you want deeper answers, I suggest you delve into the Bible itself. To wonder if Jesus could have died another way is a sidestep topic. He died the way he did, and that saves us from punishment. Can you think of a better way he could have died? Or let's put your argument another way:

I have a sailboat. Could I sail it without sails? Maybe. You could challenge me to sail it mastless. But which is better, with sails or without sails?

Even if we concluded Jesus could have died in a less impactful way, what would that accomplish? Atheists-0. Theists-0. Idle chatter-1.