Is one who swore not to return to masturbation, but then returned to it, considered an infidel (kāfir) in the sight of Allah, despite his adherence to obligatory prayers and acts of worship? Do its physical and psychological effects disappear? And is his repentance accepted?

Masturbation is forbidden. Breaking a covenant with Allah Almighty necessitates an expiation for an oath (kaffarat yamin (definition)), and an expiation for an oath is required for each instance of breaking the covenant. A promise made to Allah does not constitute an oath and therefore does not entail an expiation. Your statement, "And if I do it a second time, I will be among the disbelievers and polytheists with Him," is a reprehensible statement. It does not make you a disbeliever or a polytheist merely by engaging in masturbation. You must refrain from such statements and hasten to repentance.