The answers above are good, but I wanted to make this distinction. You untie knots that are either purposely tied, say on a boat, or accidentally formed a knot, like a shoelace. You untangle a jumble of ropes or hoses. These were not purposely tied into a knot, the ropes/hoses just got all jumbled together and you have to untangle them before you can use them. Unravel is used when you have multiple strands or strings of something, like a hair braid.

All of the examples you gave are grammatically correct so yes, they're interchangeable. They could all be used, but the one that sounds most natural and the one that is used most often would be "untie a knot".

I second Mojave's explanation. Another way of finding out the answer is to put the verbs in the positive sense. You tie a knot. We will never say "tangle a knot" or "ravel a knot". To tangle is generally an accidental action, and the result is a confused mess. To ravel is, funnily enough, almost the same in meaning as unravel. To ravel means to separate strands in an orderly fashion. You would only add "un-" if you had a confused mess to begin with.

They all sound natural. It depends on the sentence on which sounds more natural though. For example: I untied a knot. I have to unravel the knot Can you untangle the knot for me But honestly you could use any of them and it still sounds correct.

Untangle suggests that the knot was tied in an odd an difficult way and would suggest that some effort went into untangling the knot Untie is more simple. Suggests that it was an easy task ad the knot was tied in a simple way and was therefore easy to untie So pretty much "untangling" is takes longer and is more difficult/ troublesome than simply to untie. However I would say that these two are pretty muchinterchangable If you say "please untie the knot" or "please untangle the knot", either way, you are asking the person to do the same thing and will have the same result. Infact all 3 are interchangeable however, unravel would sound quote unnatural in everyday speech. I almost never hear anyone say they are unraveling a knot but if they did say so, I would still understand what they meant. I've heard unravel being used in a differe way for exams when people say "the situation is unravelling". Either way, I would generally use untie or untangle