This is a great resource that'll be useful to many people. To the author, thank you for taking the time to write these down and put them online. It would be a fascinating sociological/psychological research project to go one level deeper and give a few variants of each response, noting the implications and nuanced differences in the connotation of each.
For example, for "answer my emails", the author suggests: "If there’s a better way to get in contact with you please let me know as I am hoping to have this resolved as soon as possible". This is a totally valid and common way to say that. However, taken literally, it's silly! The person would need to read this email in order to know to suggest a different way to get in contact with the sender. Who's going to reply and say (basically) "I got your email, but please contact me with the same inquiry on (different contact method)"?
Another way to rephrase "answer my emails" would be to say "Just checking: did this email get flagged by your spam filter?" It's similarly facially silly: if it was flagged as spam, then this followup would likely also be flagged as spam, so the recipient wouldn't see it. But it signals to the recipient that you don't/won't consider their slow reply to be their fault, which could increase your likelihood of getting a reply. And other things (eg the recipient doesn't want to be seen as having a dumb spam filter, short 1-question emails get the highest response rate, the recipient now has an opportunity to immediately help clear up a simple question--was the email flagged as spam--which is an immediate reward for them, etc.).
Ah, the infinite complexity of human communication.
For example, for "answer my emails", the author suggests: "If there’s a better way to get in contact with you please let me know as I am hoping to have this resolved as soon as possible". This is a totally valid and common way to say that. However, taken literally, it's silly! The person would need to read this email in order to know to suggest a different way to get in contact with the sender. Who's going to reply and say (basically) "I got your email, but please contact me with the same inquiry on (different contact method)"?
Another way to rephrase "answer my emails" would be to say "Just checking: did this email get flagged by your spam filter?" It's similarly facially silly: if it was flagged as spam, then this followup would likely also be flagged as spam, so the recipient wouldn't see it. But it signals to the recipient that you don't/won't consider their slow reply to be their fault, which could increase your likelihood of getting a reply. And other things (eg the recipient doesn't want to be seen as having a dumb spam filter, short 1-question emails get the highest response rate, the recipient now has an opportunity to immediately help clear up a simple question--was the email flagged as spam--which is an immediate reward for them, etc.).
Ah, the infinite complexity of human communication.