/kim- / किम्

The pronoun nounbase /kim- means "who?", "what?", "which one?".

It keeps its orrignal form **kim किम् in two situations. (A) when neuter before /su or /am —

/kim- n + /su OR /am → **kim किम् "what?"

kiG karoSi किं करोषि "what are you doing?"

phalaG kim फलं किम् "what's the result?"

and (B) ibc, as in —

kim-vyApArA किम्व्यापारा "what's her job?"

kim-artham किमर्थम् "what for?".

When ibc, it is always **kim किम् irrespective of gender.

Outside of those two situations, rule kimaHkaH will replace /kim- with ka- कॱ. So, most of the time we may fancy that **ka- कॱ is a nounbase —

/kim- before any /sup
→ !**ka- कॱ "what?", "which one?"

and when feminine takes /TAp —

/kim- f before any /sup
→ **ka- कॱ + /TAp by ajAdyataSTAp /

→ !**kA- काॱ "what?", "which one?"

Examples —

/kim- m + /su
→ **ka- कॱ + /su
→ !**kas कस् m "who?"

kas tvaG kas tava pitA कस्त्वं कस्तव पिता "who are you? who are you the son of?"
/kim- f + /su
→ **kA- काॱ + /su
→ kA का by halGyAbbhyodIrgh...
→ !**kA का f "who?"

kA tvaG kas tava pitA का त्वं कस्तव पिता "who are you? who are you the daughter of?"

What does the kim किम् in kiJ carasi किं चरसि mean? That sounds to me like "what do you walk?". It does not make any sense.

The word **kim किम् may also mean "Why?" or "how come?",

kiJ carasi किं चरसि "Why are you walking?"

or maybe just "are you" or "aren't you?" (tag question marker, qq(see wikipedia on Tag_question)). Sometimes just "wow!", as in

kiM vaidya-makair anugRhito 'smi किं वैद्यॱमकैरनुगृहितो ऽस्मि "Why, doctor McCoy, thank you!".