Concerning the Torah, Hillel summarized it as, That which is hateful to you, do not do unto others
All the rest is explanation
Go and study it. Hillel was not downplaying any of the Torah but expressing the spirit of it. The man who had asked the standing on one leg question had previously been run off by Shammai who was much more concerned with the letter of the law.
What Jesus opposed was the obsession with the plethora of man made laws. Mark (Mk 7) and Matthew (Mt 15) illustrate this in the confrontation with the Jerusalem Pharisees. They criticize the absence of the hand washing ritual before eating. Rather than a sanitary measure, this was to ensure that tithes given to the priests would not ritually contaminate the priests. It was to be done all the time, not just prior to giving tithes. This is not explicitly in the Torah but was an elaboration of the requirement for bathing before presenting tithes to allow more common tithing. It is this kind of often self-serving obsession with rule making that Jesus opposed.
Jesus then proceeds to lambast the Pharisees over the korban practice. Korban simply means sacrifice. In this context, it referred to the pledging of property to the Temple, e.g., on ones death. This was interpreted to mean that one could never use that property for any other purpose even if ones parents desperately needed help. Jesus pointed out that the man-made rule contradicted the God-given command to honor ones parents. We have already seen that Jesus considered the action commandments of the Decalogue to be of primary importance.
Deuteronomy 24 specifies the rules for divorce, primarily that the husband writes a bill of divorce and gives it to her wife. By the time of Jesus, these rules had become elaborated in legalistic fashion. In Mark (Mk 10) and Matthew (Mt 19) Jesus speaks against not only the elaborations as might be expected but against the idea of divorce itself. He leaves only the wifes adultery as a legitimate qualification. As justification he cites Genesis (Gen 2) that man and woman are joined as one flesh. Here is a stronger than usual case of Jesus cutting through legalisms and getting back to basics. (Amos would have been proud.) It should be noted that Jesus was not advocating stepping outside any scriptural laws but making them stricter in accordance to what he saw as the original intent of God.
I do not see Jesus defining adultery. He does comment that a man who divorces his wife for reasons other than fooling around and marries another commits adultery and that if she remarries it is also adultery. Jesus is noting that sex outside of (legitimate) marriage is adultery but does rely define adultery. What about unmarried people having sex? Is that adultery? Cannot say from these passages.
I also do not see how this relates to internalizing love. Please explain.
Looking at the several stories concerning kosher dietary laws and other practices, it seem to me that Jesus never intended to step outside any legitimate scripture based requirements, only the mad-made elaborate elaborations. He saw these as shifting focus away from true righteousness.
Mark (Mk 7) has Jesus declare all foods allowable. We may note that Matthew, champion of every jot and tittle of the Law, omits that comment. Luke omits the entire section, possibly because the back and forth about Judaic legalism would be too confusingly unfamiliar to Lukes mainly Gentile audience.
Paul in Galatians (Gal 2) relates his confrontation with Peter (Cephas). When Peter is in Antioch he eats with Gentiles. What he eats is not specified but eating with gentiles alone is against strict kosher law. When representatives from James in Jerusalem arrive, Peter no longer eats with gentiles. Paul calls him out on this.
In Acts 10 Peter states that he has never eaten anything impure but a vision from God tells him it is OK. Likewise when he enters the house of a gentile. In Acts 11 when Peter relates this story the Council of Jerusalem agrees that gentiles can also be Jesus followers. It is not clearly stated but the implication seems to be that gentiles need not follow kosher law to be Jesus followers and that Jews who were Jesus followers were also exempt.
Galatians and Acts both agree that the original core belief of the Jesus movement was that it was a totally Jewish one, following kosher law and excluding gentiles. But how could it be if Jesus said that kosher dietary law was obsolete? It would appear that Mark which was written after Pauls epistles is inserting this remark by Jesus to ex post facto justify gentile inclusion, already an accomplished fact when Mark was written. We are then led to the belief that Jesus never intended the movement he started to be anything other than Jewish.
Hope you got a good rest.