Yes, one must keep the commandments of God, which are summed up in Mark 12:30-31: "You shall love the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength . . .You shall love your neighbor as yourself. There is no other commandment greater than these."
Christ did not come to abolish the law, but to fulfill it (Matthew 5:17). Christians are not obligated to keep kosher, sacrifice animals, and such, but this does not mean that they can commit idolatry, adultery, theft, murder, etc without consequence. The Gospel and the rest of the New Testament are replete with admonitions that our conduct in this life (i.e., our keeping or breaking of the commandments) will effect our eternal destination.
As for the new covenant, we believe that it is being part of the body of Christ, sharing in His death and sharing in His resurrection. This is intimately connected to the Eucharist; at the Last Supper, Christ speaks of the "new covenant in my blood" (Luke 22:20)
I guess the critical distinction is between "eternal destination" and "eternal reward". I assume you are referring to the very many passages along the lines of "... and the adulterer will never see the Kingdom of Heaven...". We would both say that this is true, unless the sinner has been forgiven.
I suppose Protestants believe that at the point of salvation, all sins, past, present, and future, are forgiven. One proof text is John 19:30 -
"30 When he had received the drink, Jesus said, 'It is finished.' With that, he bowed his head and gave up his spirit."
The literal Greek word means "paid in full". From what you have said, it appears that Catholics believe in a partial works-based (keeping of commandments, baptism) salvation. In Catholicism, can salvation be won and lost on a week-to-week basis dependent upon one's confessional status? What about sins committed after the last confessional before death? I think that the Last Rites solves some of this problem, but clearly not every good Catholic has the opportunity to receive them before death.
Also, with a partial works-based salvation model, how do Catholics interpret Ephesians 2:8-9? -
"8 For it is by grace you have been saved, through faith—and this not from yourselves, it is the gift of God— 9 not by works, so that no one can boast."