I think you are confusing English Grammar with Greek Grammar. Greek Grammar has SEVEN (not six) uses of the perfect. Sure there are overlaps from Greek to English uses of the Perfect.
In Greek verbs, time is only significant in the indicative mode and type of action is always more significant. In 1 John 5:1 the Greek verb is a Perfect Indicative passive. The passive voice demonstrates the person who is the object of new birth is not participating in that action but is the object of the action as it is the action "of God" not of man. The perfect tense is found in the indicative mode and thus the normal use of the indicative refers to a completed action in past time that continues as a completed action up to the present moment of writing. Remember, time is a factor in the indicative mode. The fact that the verb refers to the new birth demonstrates it cannot possibly be a continuing or incompleted action as it is elsewhere decribed as an Aorist tense puntillar created completed action (Eph. 2:5,10;4:24; Col. 3:10). Hence, it cannot possibly be intepreted a progressive continuous present tense incompleted action, so that eliminates numbers 1 and 4 in your options. The new birth is a punticilar completed action in the past (indicative mode) and so that eliminates numbers 3 and 6.
That leaves numbers 2,5. The new birth is not progressive in action. The use of the simple past perfect refers to a completed action in the past that stands complete from the past point of completion right to the present. Hence, the only possible choice that fits the character of the new birth is number 2 or the simple past perfect - completed action at some point in the past, which continues as a completed action.
Finally, this perfect tense verb is used with the present tense participle translated "believeth." The action of the participle in relationship to the action of the verb is the issue. If the participle were a completed action tense then it would indicate that action occurred previous to the action of the verb. If the participle were a future action tense then the action occurred after the action of the verb. However, the tense of the participle is a present tense action which demands it occurs SIMELTANEOUS with the action of the verb and that is precisely why the King James Translators use the present tense "is" to show this simeltaneous action.