The Temple curtain is torn in to, this is why every Christian rite that uses a curtain, whether only a small one before the royal doors of an iconostasis (like the EO, Copts, etc.) or a large one all across (like the Armenians, Syriac, etc.) retracts that curtain and reminds us that it is open to us.
It is also very important to note that in the Old Testament, sacrifices were given by the people and taken into the Holy Place to be offered up to God, but in the New Testament, after we offer our sacrifice (bread and wine) Christ Himself comes back out to us and gives us His sacrifice...the body and blood of the Eucharist. The curtain serves to remind us of the Old Testament, and it shows forth the New Covenant of Christ with that imagery.
As far as the general separation of the altar and the nave...just because Christ has come doesn't mean that there aren't still holy places, priests, sacrifices and the like. Christ Himself said He came not to abolish the Law and the Prophets but to fulfill them. We maintain the symbols, patterns and traditions of the Old Covenant because they are still with us, simply fulfilled in Christ. What was worship in type and shadow then is now worship in spirit and truth.
Exactly. And also, we must not forget the symbolism inherent in preserving a separate nave and sanctuary (i.e. altar). Their meeting is the meeting of heaven and earth, of holiness with sin and a fallen creation. The doors to the Kingdom are always opened from inside never from outside showing Christ coming to us. Just because Christ rent asunder the curtain does not mean that there is no longer separation or exile between sinners and the Heavens.