a. This would be effective for letting the students know that she encrypted their name, but it would also allow anybody with her public key to see their classmates identities.
b. If she encrypted names with her public key, it would mean nothing because only she could decrypt them to read them. The kids would be so sad.
c. Using a single shift cipher, the identities would be very insecure, because as soon as one student knows the shift (so that they may decrypt their own name), they all know the variable needed to decrypt everybody elses name. It would also be prone to counting the length of each word in their students name, making it easy to match up.
d. Even if she used different shift cipher, it would be trivial for a bored student to spend time brute forcing the single variable needed to decrypt another students name. They would have to repeat this process (26 times at most) to figure out a new name. Also prone to name letter counting.
e. A substitution cipher is slightly stronger, because its not as easy to brute force as a simple shift cipher. Statistical analysis wouldnt really work, seeing as they are formal names and not the English language. Also prone to letter counting.
f. This would be good, because each person can get their grade, without having to share a key with each other. The key block-cipher is definitely strong enough to prevent a casual brute force.
g.
1. Private key block cipher its the only truly effective way out of the whole group. No need for sharing keys.
2. Substitution cipher Brute forcible, but not easily.
3. Shift cipher (different ciphers) Still easy to crack, but slightly harder than a single shift for all the students.
4. Shift cipher (same cipher) Even if she didnt share her key with the class, one of them could easily figure out the shift and share it with everybody else.
5. Encrypting students name with her private key Not very good for keeping their names secret, but at least they can authenticate her identity.
6. Encrypting students names with her public key That means only she can read the grades. Inaccessible.