One image runs through this whole family: a hollow, an empty space. Literally it is חָלָל, outer space and any cavity; the flute is a hollow tube, the window a gap in the wall, a link a hollow ring of a chain. Then the idea turns moral: to profane the holy is to hollow it out, to empty it of sanctity, which is why secular (חִילוֹנִי) sits in the same family. Empty space and emptied holiness are the same root. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Modern Hebrew lexicalizes the moral side mostly in pi'el: לְחַלֵּל, to hollow the holy out, to profane it. The literal "empty space" side lives almost entirely in the nouns. Other binyanim are not lexicalized here. (Note: this is the "hollow / profane" ח-ל-ל, kept separate from the "play a flute / begin" senses some of these words also touch.)
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.