Step 1: Know what the Solvay process makes.
The Solvay (ammonia-soda) process is used to make sodium carbonate, $Na_2CO_3$. A key step is precipitating sodium hydrogen carbonate, $NaHCO_3$, because it is only slightly soluble and drops out of solution.
Step 2: Check the first statement.
The first option claims $K_2CO_3$ can be made by the Solvay process. The matching potassium salt, $KHCO_3$, is far too soluble in water to precipitate out. So this route fails for potassium, which makes the statement wrong.
Step 3: Check the byproduct claim.
The second option says $CaCl_2$ is a byproduct. This is true, since the overall process leaves calcium chloride behind.
Step 4: Check the basicity claim.
The third option says aqueous $Na_2CO_3$ is basic due to hydrolysis of the carbonate ion. This is correct, as $CO_3^{2-}$ reacts with water to give $OH^-$.
Step 5: Check the heating claim.
The fourth option says heating $NaHCO_3$ gives $Na_2CO_3$, $CO_2$ and water. This is the correct thermal decomposition.
Step 6: Pick the incorrect one.
Only the first statement is false, so it is the incorrect statement asked for.
\[ \boxed{K_2CO_3 \text{ can be prepared by solvay process}} \]