Well, I am preparing to play a Cold/Terror adventure (Rime of the Frost Maiden), so I was looking at this Cantrip and some questions was brought up:

1- "You instantaneously light or snuff out a candle, a torch, or a small campfire."
So, will this work even if the wood are wet?

2- "You instantaneously clean or soil an object no larger than 1 cubic foot."
So, imagine that some juice is spilled on your robe... Likely you can use this spell to remove all of it, right!? But, if what spilled was Water... Can you clean the of Water from a pants or a piece of wood?  (In a sense, its seems similar to the Juice example, but with water sounds "weird").

3- "You chill, warm, or flavor up to 1 cubic foot of nonliving material for 1 hour."
About the warm part, will you make the thing warm or give it some heat? My point is: If I use it on my robe, since the spell last for an hour, can I say it will be warm even on the open?
Going further, if I use it on an Ice Cube will it instant melt since H2O "can't exist" on solid form at that temperature?

Thanks for you time and attention!

PS: Our table is RAW heavy, I mean, of course we adapt somethings but in general the DM likes RAW.

"1- "You instantaneously light or snuff out a candle, a torch, or a small campfire."
So, will this work even if the wood are wet?"

This function is essentially equivalent of a lighter. If you could light that candle, torch or small campfire using a lighter then yes, if you could not then no. It's a brief spark of flame. It doesn't create magical fire - it creates a spark to ignite something flammable.

"2- "You instantaneously clean or soil an object no larger than 1 cubic foot."
So, imagine that some juice is spilled on your robe... Likely you can use this spell to remove all of it, right!? But, if what spilled was Water... Can you clean the of Water from a pants or a piece of wood?  (In a sense, its seems similar to the Juice example, but with water sounds "weird")."

To an extent sure. It requires a looser definition of clean. The idea of the cantrip is simple bits of minor convenience. So, yes, drying spilled water is fine. You wouldn't be able to dry something completely waterlogged or dehydrate plants or anything, but a simple spill? Sure. Likewise, you could give "water stains" to things but you wouldn't be able to create water you could drink. If you want to more thoroughly dry something or create drinking supplies of water, the spell Create or Destroy Water is what you're looking for. 

"3- "You chill, warm, or flavor up to 1 cubic foot of nonliving material for 1 hour."
About the warm part, will you make the thing warm or give it some heat? My point is: If I use it on my robe, since the spell last for an hour, can I say it will be warm even on the open?"

You could warm your clothes, certainly. 

"Going further, if I use it on an Ice Cube will it instant melt since H2O "can't exist" on solid form at that temperature?"

Normal, non-magical, ice? You can cause it to start to melt. It wouldn't melt "instantly" but over the course of several seconds, sure. Think of a cup of tea - not hot enough to scald your flesh, but still warm enough to have steam and quickly warm you up. Now pour that on ice. That's the effect you're producing. The ice will definitely melt in seconds, but not quite instantly. It's "warm" not "hot". 

"PS: Our table is RAW heavy, I mean, of course we adapt somethings but in general the DM likes RAW"

The full extent of what you can do with Prestidigitation requires your DM. It's designed to be a variable tool for many forms of minor convenience. The books are built with common everyday speech, not full of technical nitpicky language. This is specifically designed to make the DM the judge, not the dictionary. 

The "RAW" isn't real RAW. Rules in D&D 5th Edition are called that for simplicity, but are not real rules. They're a guideline and malleable groundwork for the DM's convenience. They're a frame, it's the responsibility of the DM to build upon them, not stick to them.

From the DMG: "The D&D rules help you and the other players have a good time, but the rules aren’t in charge. You’re the DM, and you are in charge of the game."

The books are rife with references about reflavouring and expanding on what is presented. Rather than asking randos on internet "is it raw" you should ask the DM "can I do this". The DM then shouldn't be rifling through books with a dictionary to find out the technical definitions of words to determine an answer -- they should just consider the idea and agree or not. If it leads to abuse or something they can always change their mind.

RAW are useful. They should not be restrictive - that's not their purpose.

Prestidigitation is one of the my favourite spells in the game, definitely my favourite cantrip; not because it's powerful, but because there is a huge amount of potential to be creative with it and add little bits of magical flavour (sometimes literally) to what your character does.

But like Cyb3rM1nd says it's not well suited to being too "RAW" focused, as it basically begs you to be creative with it, and it's both weirdly specific and a bit vague. To try and give some examples:

• The first bullet point says you can "light or snuff out a candle, a torch, or a small campfire", but it doesn't say "or similar", so what about an oil lamp? RAW you couldn't, but it seems reasonable that this feature of the spell is just intended to be a convenient alternative to fishing out your tinderbox and lighting a small flame yourself. But what about lighting a fuse (something designed to be lit)? What about lighting the kindling in a large bonfire to get it started (but not lighting the whole thing in single turn)? There's a possibility of this feature running away from the DM if they allow a player to go too far with it and use it to start very tiny fires wherever they want (since those can quickly become very large fires), but there are lots of basic utility uses that should probably be allowed.
• Clean/soil/chill/warm/flavour affects up to a one foot cube, but are robes smaller or larger than a one foot cube? I think the answer is probably smaller, because you can fold robes up (i.e- they're smaller by volume), but in RAW it could be argued that worn robes are taller than a foot so not eligible, but this would mean you couldn't clean the hem of your robe after walking down a muddy road and other things a caster would definitely use this spell for. Working out the volume for things on the fly isn't exactly convenient, so usually what matters is what you're trying to do. Cleaning muck off robes or making your friend's ale taste like earwax and similar should be fine, but I think the DM really has to rule on a case-by-case basis.

I mean these are basically the same points you already identified, as I think the others have fewer edge cases to them, but yeah, the important thing for you and the DM to keep in mind is that this a practise spell for performing minor conveniences and parlour tricks; for nearly all the effects the main benefit is that it saves you time, as instead of having to walk over to a torch sconce to light it, you can just snap your fingers and it's done, instead of scrubbing clothes by a river you can just magic away the stains and so-on. As long as what you're doing fits within that kind of level of power then I think creativity should be encouraged, if not mandatory.

RAW or not, these are all deliberately worded vaguely so that it's the DMs call.

It's up to them to decide what "soil" or "warm" mean so you should really just ask your DM this question because that's the only interpretation that is going to matter.