Yes, I understand it needs to be mutual.
Going to try and answer them one at a time.
Lets say they agree to celibacy for a time, but one starts to get angry and begins to feel denied?
It would seem in that situation that its no longer truly mutual. Sometimes spouses agree to something and then realize, for what ever reason, they can not hold to there side without some emotional damage that is not necessarily within their control. They would need to talk about the situation and how they feel and try to come to an agreement on how to proceed.
What if that partner falls into a pattern of sin?
Thats one of the reasons spouses can not deny each other the marital right with out serious reason. To avoid sin is a just reason to ask for the marital right as well and can not be taken lightly.
What if there are situations where the woman is not satisfied sexually with her partner, as a result of an ED issue, and the husband does not recognize that it is a contributing factor the to his spouse not wanting sex anymore?
That sounds like a lack of communication. In this case I would suggest a good Catholic Marriage councilor that isn’t gong to recommend any activities that are immoral.
What if the woman was sexually abused or raped in her childhood and does not find sex with her husband appealing because of the emotional & psychological scars?
Again I would suggest a good Catholic councilor, probably both a marriage councilor and a personal councilor. Those things can be healed.
What if the husband does not want anymore children, or vice versa, and live by the “you don’t want a baby, don’t have sex” theory, and do not trust NFP
Well the problem with that theory is its not even supported by the Church. The Church does not teach that sex is just for making baby’s, it also teaches that sex is for the unification of spouses, its the renewal of there wedding vows. If a couple is done having babys, for just reasons, there is no Church teaching that the couple must live a celibate life, its quite the opposite actually.
Not trusting NFP is an totally different issue. I would suggest research. Look at the different methods and the failure rates. Normal use NFP is about 80% effective, thats only because it includes people that kinda sorta use it to space kid and get to a point where they are only half heartily avoiding and start braking all kinds of rules

Perfect use its effectiveness of like the Sympto-Thermal method is 99.7% or something like that. There are 2 other methods I can think of off the top of my head, Billings and Creighton, each one works in a different way. With in a couple months of charting it is possible to find days each month that baring a literal miracle it would be impossible to conceive.
What if one spouce does not love the other in a sexual way?
Well I would assume at one point they that spouse did love that way or they wouldn’t have gotten married

This also sounds to me like a marriage councilor issue. All marriages have ups and downs, sometimes the downs need a bit of out side help. So far, my marriage, has had one major bad point, counseling did wonders for us. What we learn has helped us reconcile many issues before they blew up since.
How can sex be unitive with these issues? Is it allowable to assume that one spouce can disregard the issues of one and demand that sex is the marital right?
Sex is unitive
despite those issues. A spouse should not disregard any issue the other is experiencing, but on the same token, a spouse should not disregard the others need for the marital right. Communication is key, spouse should talk about their feelings and emotions on how there sex life, or lack there of makes them feel.
I know these are huge “what ifs” but they are nonetheless real issues that many couples face in there sexual union…
Not overly huge what ifs

I know people who have gone through some of these issues form one extent or the other.