Yes, in a word. The proto-Indo-European interrogatives began with /kw-/, and they were all related because they were all essentially case-forms of a single word: kwis? 'who?' contained the active ending /-s/, and kwid? 'what?' had a neuter element /-d/ instead.
Other interrogatives 'why?', 'how?' etc. are originally oblique cases 'for what?', 'with what?'.
The normal sound-changes applied in the different branches.
Latin /kw-/ became /k-/, inherited in all its descendants (qui, que, che etc.).
In Germanic it became /hw-/, and yes this is Grimm's Law. The brothers were the first to lay out the regularity of the sound changes. These have become /w-/ in most varieties of English (still /hw-/ in Scots and older American) (and /h-/ in who, how but I'm not sure why), and /v-/ in German (wo, was, wie). It's still a cluster in Icelandic (hvadh).
The /kw-/ became /t-/ or /p-/ in Greek depending on the following vowel: tis, ti, pu, pote.
Now 'query' and 'question' come from a Latin verb root quaes-, which I would guess is from the interrogatives, i.e. originally meant 'to say "what?"', but I can't confirm that.
