Step 1: Use the Hawkins formula for skin factor:
The Hawkins formula relates the skin factor to the ratio of the original permeability k to the altered permeability ks in a damaged or stimulated zone of radius rs around a wellbore of radius rw. The formula is $s = \left(\frac{k}{k_s} - 1\right)\ln\left(\frac{r_s}{r_w}\right)$. Since $\ln(r_s/r_w)$ is always positive for $r_s > r_w$, the sign of s depends only on the sign of the bracket term.
Step 2: Apply the formula to formation damage:
Formation damage reduces the near wellbore permeability, so $k_s$ is smaller than $k$, which means $k/k_s$ is greater than 1. The bracket $\left(\frac{k}{k_s}-1\right)$ becomes positive, so s comes out positive. A positive skin factor confirms that formation damage increases the skin factor, matching statement C.
Step 3: Apply the formula to hydraulic fracturing:
A successful hydraulic fracture creates a very high conductivity path around the well, which is equivalent to making $k_s$ much larger than $k$, or equivalently increasing the effective wellbore radius $r_w$ to a much larger fracture half length. In the Hawkins style view, $k/k_s$ becomes less than 1 so the bracket becomes negative, and in the effective wellbore radius view a larger $r_w$ makes the ratio $r_s/r_w$ smaller pushing the logarithm term down. Either way the calculated skin factor becomes negative, confirming that hydraulic fracturing decreases the skin factor, matching statement B.
Step 4: Conclude:
Since damage always pushes skin positive and successful stimulation such as fracturing always pushes skin negative, the correct statements are B and C only.
Final Answer:
\[ \boxed{\text{B and C}} \]