I have never understood monogamy from an evolutionary or practical or emotional point of view.
From an evolutionary perspective, it probably evolved as a by-product of social monogamy.
From a practical perspective, it makes a ton of sense for ecological/economical points of view. For men its usually practical because male-male competition for fecund mates is very high. For women it made sense in the Paleolithic because they could increase the probability of bi-parental investment (it is another debate about what sense it makes for women today in the developed world).
From an emotional perspective, that is a personal opinion that everyone should be free to make on their own. I personally like the idea of finding someone that I can bond with long-term. However, IMO whatever someone feels comfortable with should be acceptable (as long as they are not purposefully hurting other people).
Insecure people insist on monogamy as way to hopefully or mutually control their partners
Many people unfortunately do this, however this is not how monogamy is practiced at its best. Monogamy can also be developed from a psychologically healthy place - not always from insecurity.
Do non-monogamous apes say, "Will you still respect me in the morning?" Do apes ever feel used?
Well, as I said above, I think you need culture to truly be sexually monogamous. Biological evolution would never really favour sexual monogamy so it is hard to say. However, studies have shown that gibbons become exceptionally depressed when their partner dies. This is probably because they formed a strong emotional bond with that partner (they share songs, feeding rituals, defend each other from predators and raise young together). They may not care about sexual extra-pair copulations. Males have not been observed to mate guard, but that may be because both partners sneak extra-pair copulations fairly well. Not sure if this answers either of your questions... I don't know how we would know whether great apes felt used. I'm guessing that they experience a range of sexual emotions that are dependent on the context of their socio-sexual system.