The moment of inertia of the rod to the center of mass is112ml * l, and the moment of inertia to the vertex is1/3ml * l. The parallel axis theorem is used, that is, the moment of inertia to the center of mass plus the square of the distance from the center of mass to the vertex is multiplied by the mass.

1/ 12ml*l+m*[( 1/2)l]^2= 1/3ml*l

The moment of inertia of a circle is (1/2)MR*R, and the vertex is (1/2)MR*R+M(L+R)*(L+R).

So the answer to the first question is as you said.

Regarding the center of mass, take 0 as the center and downward as the coordinate axis, divide the rod and the circle into two parts, multiply their center of mass by their center of mass coordinates, sum, and then divide by the sum of the areas of the two parts.

r(c)=mL/2+M(L+R)/(M+m)，

Let's use the parallel axis theorem to calculate the moment of inertia again.