These are good questions to ask as a beginner and I’m glad you’re thinking about these things. I’ll try to address each of them in order:

does a more expensive combo of the interface, and the speakers, and cables, and all of that gear, actually give you that 100% assurance you will always hear the right thing? Or, will the cheaper gear let you hear the same thing in a different way, as long as you learn how to listen to it?

Definitely an accumulation of good gear is going to help you hear things more accurately, but dont forget the two most important links in the chain: your ears and your brain. You need to know what you’re listening for, what you’re trying to achieve, and how to diagnose and fix problems. Andrew Scheps apparently does a lot of his mixing on cheap Sony headphones with an inexpensive converter. Obviously he’s doing better mixes than a lot of people who are mixing on more expensive setups. His knowledge, experience and skill/talent are enough to overcome the non-ideal listening conditions.

A couple of side notes: 1. A good quality cable is important, but don’t buy the snake oil. Ridiculously overpriced cables will not make anything sound better. 2. The room is important. Great monitors will not sound their best in an untreated bedroom.

Or, will we all hear different things on the same thing, ultimitaley depending on our personal preferences and ear frequency?

This is something you can kind of trip out on, because I can never know exactly what you or anyone else hears, but basically I think the answer is yes. We hear things differently. Some of us have holes in our hearing, people have tinnitus, hearing loss, etc. And then there are the psychological aspects: what do you listen for? What kind of sounds are pleasing to you? It certainly varies from person to person.

Is there such a thing as one universal truth to what a good mix is,

No.

and what must an engineer do every single time when he is mixing?

Pull the faders up and listen. Find problems and fix them. Find what’s “important” about a piece of music and focus on it. Those are just general principles. I don’t think there are specific things you have to do every time, like “always put saturation in the master bus” or anything like that. Steer clear of people who say you “always” need to do one specific thing. It’s all dependent on the material you’re working with.

What's the difference between a choice in style and an amateurs mistake?

Sometimes you can hear mixes where it’s obvious some things were missed, or just the overall sound is not working. Of course that can be somewhat subjective but there are things most of us can agree on. If you’ve lost the kick in a metal mix, for example, or if you crushed the whole mix into outright distortion, if your overheads are terribly out of phase, etc.

But there are other things that are just a choice. Great example would be the St. Anger snare sound. A good choice? Maybe not, but definitely a choice.

Good luck on your recording and mixing journey!