Hi Deuteronomy,
Much of the OT still seems a mystery to me and usually I don't try too hard to answer about the significance of most OT topics...but God has started to open my eyes and understanding to SOME things, so I'll do my best to answer your questions using what he's shown me so far. Please bear in mind that I'm not claiming these to be fully comprehensive answers...just "through a glass, darkly".
In answer to your first question, I think he gave the commandments regarding sacrifices for at least 3 reasons:
1. To see (find out) if they would HEAR his voice. A person hasn't truly heard the message until they've done the action (because part of the message is contained in the doing). This relates to the 1st commandment in so many ways.
2. To show them the pattern of what the true sacrifice MUST accomplish. This is not a single-step, quick fix slaying; but rather a very detailed, very deliberate set of rules which must all be satisfied or else the sacrifice will not be accepted.
3. To teach them that redemption is NOT FREE...the cost of sin (and price of redemption) is HIGH. God was showing them that although they will be receiving the benefits of the sacrifice freely, the one MAKING the sacrifice (the one who IS the sacrifice) will be paying a great price. This is not only regarding the Messiah. Don't overlook what those OT animals were giving up. And don't underestimate the cost of what "come, take up the cross and follow me" really means. Matthew 16:24, Mark 8:34, Mark 10:21, Luke 9:23
In answer to your second question about what atoned for the sins of the OT people:
There is only one sacrifice that truly atones for sin...and that is Jesus (because he is the one true sacrifice for sin, forever... Hebrews 10:12, Heb 7:27, Heb 9:26, etc). However, the question still remains (even if not directly spoken) of "How does one attach him-or-herself to this sacrifice in the OT? because obviously some receive and walk in the benefit of the sacrifice... and some do not."
I've been talking about how it is done in the NEW testament, but you're asking about the OLD testament. I think it is worth finding out and discussing, but I personally don't have a clear enough understanding (nor the time to write it here) at this time. I do however know that it pre-dates the sacrifices, pre-dates the law, and pre-dates the Abrahamic covenant of circumcision. It's got something to do with promise, faith, and the heart of man (what a particular man truly wants good/bad regardless of his level of knowledge at the time).
Love in Jesus,
Kelby