b) The answer to this part may depend on what ASCII characters you mean. The upper limit is 7 bits per character and includes numerals punctuation and other signs. 7 bits have a range of 128 values. If n is the number of characters, then 128ⁿ must be less than the modulo, which is 62663. 128²=16384. But 128³=2097152, which is bigger than 62663. So the maximum on this basis is 2. This is my best guess.
If the ASCII codes can only be upper- and lowercase letters then, since there are 52 of these, 52²=2704, but 52³=140608, which is bigger than 62663. So, even with this reduction, only 2 letters can be sent in one go. So the answer is 2, however the characters are encrypted.
Another way to answer this is to count bits. ASCII codes are 7 bits long and N is 16 bits long, so only two will fit. 52 is 66₈ which is 6 bits long, so only two will fit.
c) e cannot be a factor of 222 or 280.
222=2×3×37, so 3 is disallowed.
280=8×5×7, so 5 and 7 are disallowed, and so is 35.
45 is disallowed because it has a factor 5 in common with 280.
I always intend to answer all parts of your questions, if I can, but to do so I need to research the subject more, since cryptography is not a subject I have studied. Also, I have great difficulty submitting answers and editing, because the system and/or the network is not working properly on this website. It has been like this for many months. In particular, editing becomes nearly impossible for lengthy solutions and I experience frequent system crashes or loss of response, extreme sluggishness, reloads, etc., so it can take a long time to produce and submit a complete answer.
In the meantime, other users have the opportunity to use their skills and expertise to answer your questions. Maybe they have a better system response than I have.
I am an ordinary user and, apart from some admin functions granted to me, I have no connection with the website and I’m certainly not a mathematics expert. (I just like trying to solve problems and to help people.) So I research and check any solutions for accuracy, conciseness and presentation to try to help those who submit questions.
I hope you will be patient as I attempt to answer your questions.