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I'm currently playing as a halfling monk who is very fond of a drink. Let's say I encountered some enemies sitting around a campfire. Through means of deception or otherwise I ingratiate myself with the group enough so that they do not consider me an enemy. (My overall plan is to attack them).

At some point I cause some sort of commotion, for example spitting some of my highly flammable drink into the fire causing it to rear up and distract those sitting around it.

I am aware that I was planning this however the enemies weren't. Would I be able to use this distraction as the basis of a surprise attack?

TL:DR Can a planned distraction caused by my PC while enemies are aware of my presence, that sufficiently distracts their attention, constitute basis for a surprise attack?

If a creature doesn't notice a threat, it is surprised by it

As per the basic rules:

The DM determines who might be surprised. ... Any character or monster that doesn't notice a threat is surprised at the start of the encounter.

I'd interpret this to mean that if a creature regards you as nonthreatening and does not expect you to attack them, it is a surprise if you suddenly attack them, because they did not notice the threat. However, it is ultimately the DM's determination as to whether or not surprise applies.

If I were DMing this kind of encounter, I would probably call for a Deception vs. Insight skill check between your character and the enemies to see if you're able to hide your intentions sufficiently well that your actions take them by surprise. I would likewise be minded to give you advantage on that check if your attempt incorporates something very distracting and confusing - like causing the campfire to flare up.

It depends

First, the one who declares a situation is a surprise to the other party is the DM. He is the one who knows what the enemies are doing, and what is the state of awareness of them.

What you describe could work. Surprised means the enemy is not anticipating an attack, or not ready for it. If I was the DM, I would describe them trying to put off the fire before it spreads, lowering their guard.

However, if they are actually anticipating an attack and constantly on alert, I might rule that some of them are not surprised, or just giving the PCs advantage on initiative instead of surprise.

Additionally, this one qualifies as a clever idea in my book, and thus might grant them inspiration (or the one who come up with the idea)

The books do not give detailed rules or even guidelines for surprise, only that:

The DM determines who might be surprised. (PHB 189)

The short section in the PHB only speaks about sneaking up on someone, but it does not seem the list they give is exhaustive.

In this case, as a DM, I personally would ask for a Charisma(Performance) versus Wisdom(Perception) opposed check. If the enemies win, they are not surprised, otherwise they are.