Phones are forbidden to be used or moved on the Sabbath unless it is a matter of human life or death. So regardless of how crucial Avram's mission is in his eyes, an Orthodox Jew (such as Rabbi Lev) would not have his cellphone on the dinner table on the Sabbath.
Both bathing and burning things are forbidden on the Sabbath. Even if the Essene managed to convince Avram that he needed to undergo a cleansing ceremony, no Orthodox Jew would agree to perform forbidden actions on the Sabbath for such a ceremony.
The concept of sinning by thought equals sinning by deed is a Christian concept. Anyone who has studied Jewish law (and Avram has studied the Talmud) would know that this concept is foreign to Jewish philosophy.