5

R. Moshe Feinstein in Igrot Moshe, Orach Chayyim V, 18 shares your puzzlement, but suggests that indeed, this is referring to the rule of the goel hadam, following the opinion that is a mitzvah for the goel hadam to avenge his relative. ומה שכתב ללכת חוץ לתחום לנקום נקמת אביו, פלא. וכי היכן מצינו שיש בכלל מצווה לנקום, אף שהוא לכבוד אביו. ואולי כוונתו בדין ...


5

In Berachot 33a (translations modified from Sefaria), Rav Ami and Rabbi El'azar say that words sandwiched between two instances of the name of God are great. Rav Acha Karchina'a challenges this, based on the fact that revenge is also mentioned between two of God's names. מתקיף לה רב אחא קרחינאה אלא מעתה גדולה נקמה שנתנה בין שתי אותיות שנאמר אל נקמות ה׳ ...


2

This is the current called Gnosticism See More nevuchim third part, [Chapter 12]. He says that the hardness of life is for those philosophers a consequence that g-d created world and humankind to take a revenge on them. But the truth is that most sufferences occuring to a man are consequence of his lack of whatchfulness. הרבה פעמים יעלה בלב ההמון ...


1

There is indeed a set of antisemitic accusations, partly stemming from Christian teachings, that "the Jewish God is a God of vengeance and the Christian God a God of love" (taken from here). I will only answer with this quote from the Rambam (Hilchot Deot 7:7) which apply to both vengeance itself and the accusations you mention A person who takes revenge ...


1

That's a great question, showing how little the Halachah deals with עבודת המידות (personal growth). Here's my personal view (backed by my rabbis) Those Mitzvahs you're talking about (נקימה ונטירה) are not the actual behaviors, but the wrongful thoughts. One is commanded to OVERCOME those, just as one is commanded to overcome physical inclinations like lust, ...


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