I can't address everything in your post point for point, but I can give my thoughts on some of it.
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Also, Lee wrote it like Randy had a thing for Natalie, which he never did. I doubt Randy thinks their relationship is a searing /people can feel the heat/ never gonna happen thing. For instance, in Wedding, when Natalie made their room arrangement clear (seperate rooms), Randy said, "I should think so."
I think that this is a matter of interpretation. Another viewer might see the same interactions between Randy and Natalie and see some attraction, and the interactions between Sharona and Randy as being something other than attraction, maybe more like a teasing brother/sister thing. In either case, neither is right or wrong and can't be proven right or wrong unless it is without a doubt addressed on the show. It's really sort of impossible to say much of anything is 100% fact when it comes to people's feelings and attractions. There have been moments with Natalie and Randy when I thought maybe they were flirting or there was some attraction and moments with Sharona and Randy that seemed like they were attracted to each other. It never bothered me in either case, as long as it doesn't get out of hand and the whole show starts to become soap opera-like.
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I also think that Sharona, by time and her remarriage to her husband, minimized the flirting/interest in Lt. Disher. I doubt that the flirty relationship she had was similar to the one she had with her mechanic or grocier (if it is she needs some help). Sha also knew Randy was interested in her by the time of Paperboy, and I can say that since she knew he was interested, if she wasn't she wouldn't have played Randy like that. That's just kinda trampy if she did...anyway...that's it. Any other thoughts?
I think that matters of teasing, flirting, attraction, friendship ect are all a bit more complex than this. A person who flirts or teases more than one person isn't a tramp necessarilly, and for that matter, Randy had attractions and flirtations with other women then and still does now. If he hasn't settled down or made a commitment to one specific person, there is no reason why he shouldn't and the same could be said for Sharona or for Natalie. If Randy never came right out and said something to Sharona (and I can't remember him ever doing so) and she never agreed to entering into an exclusive relationship with him, then she isn't doing anything wrong to flirt with other men for any reason she wanted to. As to whenther she was playing Randy or not after Paperboy, he denied ever writing that ad with any interest whatsoever in her. Even this, though, is an example of how two people can view the same set of circumstances and form different views of them.