To have a dust-up

to sort things out
to squabble
to settle disputes
to have arguments
to have a beef with someone
to turn on each other
to have it out

to settle scores?

To fight

спасибо всем, но я в растерянности))

Выяснять отношения в основном же употребляется в смысле «ссориться», правильно?

ну, до ссоры может и не дойти. to squabble - ругаться, ссориться. to sort things out - устойчивое выражение. If you sort someone out, you make them realize that they have behaved wrongly, for example by talking to them or by punishing them.

This is so confusing. Everybody is offering opposing meanings: FIGHTING/ARGUING is the opposite of SORTING THINGS OUT. So what does this actually mean? Can you put it in a snippet?

The was I see it, there are at least two meanings of that: the literal one that can be close to sorting things out and the figurative one that implies fighting.
(1) Из лекции психолога:
Чтобы в семье царила гармония, супругам необходимо научиться правильно выяснять отношения.
(2) — Что с тобой? Ты сегодня весь день на ходу спишь?
– Да этой ночью совсем не удалось поспать. Соседи так бурно выясняли отношения, что под утро пришлось даже полицию вызывать.

(1) In order for there to be harmony within the family, it is imperative that couples learn to properly sort things out. (2) - What’s with you? You’re like a zombie today. - Yeah, I didn’t get a wink of sleep last night. The neighbors’ arguing got so heated that the police had to be called out this morning.

So I guess it basically means to talk things through with varying levels of intensity?

Yes))

Улий. спасибо!

не за что))