Given the importance of the hash function's characteristics, how safe is Lamport's OLP algorithm?

Does a hash table of size m always have the same number of linked lists? I've been trying to understand the function of a hash function, but I just can't seem to get it. Give a case study to demonstrate your point.

How secure is the OLP approach developed by Lamport, taking into account the qualities that are important to the hash function?

a. What characteristics are needed in a secure hash function?  b. What is the role of a compression function in a hash function?  c. Suppose H(m) is a collision-resistant hash function that maps a message of arbitrary bit length into an n-bit hash value. Is it true that, for all messages x, x’ with x ≠ x’, we have H(x) ≠ H(x’)? Explain your answer.