When valuing a callable or putable bond using the tree, if the coupon pays SEMIANNUALLY, we divide the the coupon rate in the numerator in half AND DIVIDE THE RATE IN THE DENOMINATOR IN HALF AS WELL, correct?

yup

WTF is wrong with me? I think im freaking out.

yup

Your question confuses me, but I’ll tell you what I know: Divide the coupon payment in half. Divide the interest rate in half (so a 3.5% rate would be a denominator of 1.0175)

Each interval will be a semi-annual period

yup