There's a structure to it, but one that relies on hefty improvisation. They explore the basic themes throughout the piece and sometimes the song changes entirely. If you want some more professional analysis, there's a lot of writing on the fourth part of that album, as its Coltranes tone poem.

But to me it seemed that the instruments were "detached" from each other when improvising, at least in "Part III" - the drummer is doing his thing, the pianist is doing his thing, without following any specific time signature. Could this be right, am I seeing it as freer than it actually is?

I'd say it really comes down to what you're used to.
To me this one seems pretty damn orderly and organized.
Don't know about time signatures, but this has a very clear pulse.

Ah, alrighty. I'm really not used to jazz, much less so-called modern jazz.

Just wait until Frown an me hit you with the really crazy stuff at some point.
Metal will sound like a ****ing lullaby from then on.

Oh boy.

You'll love it.

Please follow the OP.