Can you help me with two short questions? Q1: How to prove that any k-regular graph contains at least k-1 distinct cycles, all of which have

Can you help me with two short questions?

Q1: How to prove that any k-regular graph contains at least k-1 distinct cycles, all of which have different lengths?

Q2: How to show that if there exists a closed walk of odd length in graph, then there is a cycle of odd length in graph?

Thank you!!!