3.A. How come in some episodes Peggy only has one scene, talking on the phone from some faraway place?

Because in real life Katey was/is pregnant. (See Subject 3.2) In the
show her absence is explained by:

    Returning to Wanker county to be taken care of / it was all a dream
    "BUCK HAS A BELLY ACHE" (606) thru "AL BUNDY, SHOE DICK" (611)

    Returning to Wanker county to take care of her heart-attacked mother.
    "SHOEWAY TO HEAVEN" (901) thru "BUSINESS SUCKS (part 1)" (905)

    Travelling to find her wayward father.
    "Calendar Girl" thru "Torch Song Duet"