Do copper (2) chloride and potassium carbonate form a precipitate?

Answer 1

copperIIcarbonate is not possible in water solutions (and decomposed quickly in air due to water vapor. What is formed in the above reaction nearly always is a carbonated or hydroxide of copperIIchloride, such as Cu2(OH)2CO3 (which occurs naturally as the mineral malachite) or Cu3(OH)2(CO3)2 (azurite). Both of these minerals are insoluble, however, it is very unlikely one would makd this by reaction of the two forms you gave. So my answer is no, the reachtion is basically impossible without water present.

Answer 2

yes.
CuCl2(aq) + K2CO3(aq) ==> CuCO3(solid) + 2KCl(aq)

Answer 3

Bob P's answer is so much more detailed than mine; however, my experience is that a ppt does form but it usually is the hydroxide/carbonate mixture. As far as I know ALL solubility tables list CuCO3 as insoluble in water.