Symmetric cipher key size vs number of rounds. Longer key = more secure cipher?
With enough plaintext/ciphertext available (sizably more plaintext than keysize), any cipher can be attacked by trying all the keys; that's brute force. Therefore, for any cipher, too short key ⟹ insecure cipher.

A common symmetric cipher design goal is that the best attack is brute force as limited by key size, within a small factor. Therefore, for a symmetric cipher meeting that design goal, longer key ⟺ more secure cipher.

A common block cipher design goal is that it is as fast as possible while meeting its security level (matching its keysize per the previous goal). Increasing the number of rounds can make a cipher more secure, but does make it slower. Hence, for a cipher design meeting its security and speed design goals, more secure cipher ⟺ more rounds.

There is no definitive method to find the adequate number of rounds. A typical approach is to examine known attacks; try to make conservative estimate of how many rounds they can break for some security level and extrapolate to the desired security level (perhaps much higher); then take the largest number of rounds found for all attacks, and then some as a design margin.

I pass at the Threefish aspect of the question.