Ok, first IANAL, best to talk with a lawyer (preferably the one represented her in the divorce). The language may need to be clarified through the court.
2) Always best to calmly talk (face to face is best) or phone. I personally don't like texting, but that would give a record if needed later (but that works both ways).
C) If talking about parenting plan times / details, DO NOT talk in any way about child support. Both are part of the divorce, but should be viewed and treated completely separate. Courts could view bringing a money issue into a time issue as an inappropriate lever, and would frown on the side trying to use it that way.
IV) My situation is different than yours. When I got divorced, my now Ex did not fight it at all. I have full custody of our two daughters (our oldest was her's from before who I adopted prior to the divorce). She is also supposed to pay child support to me, although that has been real sporadic. When we need to deviate from the parenting plan, we contact the other soon as we know we need to change it, and we work it out. So I have never really had to worry about nit-picking the plan and dragging the other into court over niggling details.
Now, to your question... quote "every other Thursday by 7:00 PM until Sunday at 8:00 PM."
In my opinion (and I could be wrong) "by 7:00 pm" is really read as "no later than 7:00". That you fiance allows an earlier pick up at 5:30ish is a courtesy, her Ex should be targeting 7pm (not later), but a little early is good. 2pm is not a little before 7pm. By the Ex's reasoning he could pick the kid up at noon, or 8am, or 3am on Thursday and be "by 7pm".
The Sunday return is the same, "by 8:00pm" is really "no later that 8pm", with a little leeway, like 7:30 to 8pm drop off. Again, the Ex's interpretation of "by" means he could drop the kid off at 2am Sunday and that has the kid home to mom "by" 8pm.
If the her Ex is going to push the semantics and not work with mom on a reasonable time window, then you will need to get with the lawyer and have the parenting plan wording redone to be specific (i.e. pick up between 6:30 to 7pm Thursday and drop off between 7:30 to 8pm Sunday) and add something like "unless previously arranged and agreed to by the other parent with a minimum of one day in advance".
Always best to work things out peacefully, but I have heard the horror stories of friends and co-workers being pulled into court over stupid stuff because the two people's emotions and hate get in the way of discussing the problem and working out a solution. If she can avoid it, stay out of court, but after she and her Ex make changes that both can agree on, they need to write it down and both sign with a original to each. I do understand that sometimes there is no choice but to get the court & lawyers involved. Especially if there is any domestic violence in the past. If that's the case then she definitely needs to run everything through lawyers. Don't escalate the situation with a face to face.
Last comment, as the boyfriend / fiance, you should NOT be a part of the negotiations, she has to work it out with her Ex (and never in front of the kid(s)).
BUT, that does not mean you are completely outside of it, just not in the middle of it.
Be emotionally supportive, discuss the strategy / plan with her prior and what to do after, but do not be in the discussion. It could escalate a situation that is already very emotional, and the Ex could view it as a 2-on-1 and go defensive / stubborn and not work with her on a reasonable solution.
Let her know you have her back, but it is her situation as one of the two parents to deal with.
Again, IANAL, this is just my thoughts & views, take from this what you will, and if in doubt go talk with a lawyer. Good luck.