related to cryptographic ecnryption

I need help with a Mathematics question. All explanations and answers will be used to help me learn.

EP2: Assume a block cipher achieving the avalanche effect is used. Does this guarantee that the encryption algorithm has the same effect?

Explain your answer (if yes, prove it; if no, give a counter example).

The avalanche effect is a property of any encryption algorithm such that a small change in either the plaintext or the key produces a significant change in the ciphertext.

No, the encryption algorithm doesn’t have the same effect,

We will take random key and random plain text and encrypt using CTR then flip one bit and encrypted again to find out how many bits are effected in the ciphertext

EP3: attached the related figure

To attack an encryption algorithm, you ask the encryption oracle to encrypt a polynomial number of messages of your choice and observe the outputs. Then, you give the oracle two messages m0 and m1. The oracle will choose one of the messages uniformly at random, encrypts it, and return the ciphertext c to you. The encryption algorithm is said to be broken if you can determine to which one of the two messages the ciphertext corresponds. Consider now the counter mode of encryption shown in the figure. Assuming the counter is 48-bit long and the used block cipher is AES (recall that AES operates on 128-bit blocks) answer the following questions:

a. Assume the counter is always zero (i.e., the counter does not change from block to block). Can you come up with a successful attack against this mode of encryption?

b. Assume now the nonce is fixed (i.e., the nonce does not change from message to message). Can you come up with a successful attack against this mode of encryption?

c. What is the maximum length of the messages that can be encrypted using this mode?

d. In the counter mode of encryption, the nonce cannot be used again unless a new block cipher key is chosen. What is the maximum number of messages that can be encrypted using the same key?