Is there any indication of exactly what and how many of the 613 Mosaic Laws are applicable to Christians? The commandments to love God with all of your heart and to love one another as Jesus loved are vague in the perspective that Jesus Christ was the totality of the Word of God, incarnate.
The answer to your question is simple, at least in principle. Jesus did not eliminate the Law of Moses, but he fulfilled it (Matthew 5:17). As Christians, we are not obligated to fulfill the requirements of the Law of Moses. This is the central message of the entire book of Galatians and is one of the major themes of the book of Colossians. Colossians 2:14-15 tells us that on the cross, Jesus took away the requirement of law-keeping. Paul continues in Coll 3:16-19 to list specific aspects of the Law of Moses disciples are not required to obey, including laws about food and drink, New Moons, Sabbaths and more.
Of course, there are laws in Leviticus, Numbers and Deuteronomy that Christians are bound to, but this is not because they are in the Mosaic Law, but because we, as Christians, are bound to obey the command and example of Jesus. We are not allowed to kill or to covet our neighbor’s wife, for example. Of course, your example of the commandment to love God with all our heart, soul, mind and strength still applies to us! However, unless an law in the Old Testament is either repeated in the New Testament, or is implied by something in the New Testament, we are not required to obey that law as Christians. I say it is not worth your time and effort to ask how many of the 613 laws we are required to obey, since that is not really the right approach. We should look to the sayings of Jesus and of the apostles to find out the “rules” of Christianity. It is not as though the laws and other things in the Old Testament are meaningless. Not at all. Proverbs has eternal and inspired wisdom. The examples of what happened and how God reacted throughout the Old Testament has great lessons for us (1 Cor 10:6-11 says this, if we needed it to be stated). Even the laws, festivals and sacrifices have meaning as types and foreshadows of what we have in Christ (Hebrews 10:1). In fact, I have written an entire book on the spiritual application of Old Testament events, laws, sacrifices and festivals. It is From Shadow to Reality, available at www.ipibooks.com