Do you think if people are happy with themselves, there will be less problems in relationships?

With exceptions in people chronically dissatisfied (there are) I personally don´t put so much enphasis in the "inner" / character / individual issues about relationships.
Said view (that may serve well other people) is just IMO too focused in each one and loose focus in the intrinsic dynamics of the couple as a loving team and it´s compatibility.
Not because individual issues are not important, but cos the relational ones are culturaly dimmised by the current psychological schools of thought.

100%
You can’t rely on another person to make you happy. They can only add to one’s life.

Yes, if you do not love or like yourself (or are not happy with yourself) then how can you love, like, or be happy with someone else>

All that should be in you first before seeking out another for a relationship, This Jery Maguire stuff of you complete me is BS. Quit looking for others to make you complete.

Usually

Problems will always show up but they will be more likely able to handle them in smart ways that has little to no negative impact on themselves or others.

Absolutely, without a doubt.

Yes !