Q: how could a blood sacrifice solve that?

God in the old testament demanded sacrafice as a way to atone for the sins of people. This goes back to Adam and Eve in the garden of Eden. When Adam sinned(not by eating the fruit, but by disobeying a direct order from the Creator) the only way this could be atoned, was by a blood sacrifice. The reason for blood? - Exodus tells us the life of a creature is in his blood. Thus the need for blood - one life in the place of another.

After many many years and many many sacrifices God saw that a more permanent sacrifice was needed. A perfect sacrifice, taking the place of all the other offers and sacrifices explained once and for all.

Q: how could God create a son and sacrifice him, and that appeased his anger??

God never created a Son. He is God. He is just as much God as God the Father is God. He has just another function, another job if you will. And remember the sacrifice needed to be perfect? Who is perfect? Without sin? Only God. And that is why only God ( the Son) could be the final sacrifice.

Q: if people just keep on being sinful, what is achieved?

If i bought you a gift, told you about the gift, but you never came to receive it from me...does it make the gift useless? No! It just says YOU dont have the benefit of the gift. God gave His life...(The gift). Atonement was made and proclaimed (told you about the gift) and the only way to have the 'benefit' (thus forgiveness from sins and a living relationship with God) is by accepting it as a undeserved gift.

Q: if Jesus died for our sins, does this mean that we can go on sinning?
In theory yes, we could. But.... If you really grasp the concept of the offer, the sacrifice and the effect on the soul...then sinning would be something that would not be done without thought and then, after realising the sin.. You would not be at peace before you have asked, begged frogiveness from God.

I see the person Jesus as a great teacher, who had a lot to give. But I do not understand this other part of it.[/QUOTE]

I believe Him to be much, much more. And this was just a very short explaination how i believe the sacrifice works. There are many other things that could (and should) be mentioned here. I am certainly no expert but i spent 2 years at a Bible college.
if these dont answer your questions, maybe i could point you in the direction of some good books.