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Let me take on your questions one at a time:
Our Lord’s death and resurrection did replace the Old Testament offerings. The best explanation of this is found in the New Testament Book of Hebrews, especially chapters 7-10.
https://bible.org/series/near-heart-god-study-book-hebrews
I’m sure that there is a relationship between the Old Testament offerings and those we find in the New, but the New Testament also distinguishes Old Testament giving and sacrifices with those in the New Testament:
Through Him then, let us continually offer up a sacrifice of praise to God, that is, the fruit of lips that give thanks to His name. 16 And do not neglect doing good and sharing, for with such sacrifices God is pleased. (Heb. 13:15-16 NAU)
The New Testament does not speak of giving in terms of percentages and specified amounts, as the Old Testament did (see 1 Corinthians 16:1-4; 2 Corinthians 8 and 9; Philippians 4). Gratitude for God’s grace is the motivation for giving. Also, it is important to see our giving as a reflection of the nature of our God. We have been saved to become partakers of the divine nature (2 Peter 1:1-4). God’s nature is to graciously give (“This is the way God loved the world . . . He gave . . .” John 3:16). It is no wonder that after the church was born in Acts chapter 2 the overwhelming response of the new believers was to give (Acts 2:41-47; 4:33-37).
I think it should also be noted that the offerings we see in the New Testament were not always “missionary support” (Philippians 4:10-16), but were for the support of those who ministered (1 Timothy 5:17-18; 1 Corinthians 9:1-14), though not without exception (1 Corinthians 9:14ff.; Acts 20:32-35; 1 Thessalonians 2:9-12).
I would have to say three things in response to this question.
Was Moses truly the only Biblical “human” to actually communicate with God one on one on earth? I don’t think it is really accurate to say this, but Moses was truly a unique man of God. In fact, God made a point of His unique relationship with Moses when his leadership was challenged by Miriam and Aaron (see Numbers 12).
Blessings,
Bob Deffinbaugh