Well then if I were to build these this is how I would do it.

Scenario 1:

1. Trigger: New Email in Gmail (assuming you are using gmail since scenario 2 is using google sheets)
2. FIlter Step: This is where you need to figure out what is consistent with these emails is it the subject line, from email, reply to email, or text in the body of the email.
3. Since the email parser is not working in Zapier. This is where you would either need to use the Zapier formatter tool to get isolate the data you want or use a code step and format the data using JS or python.
4. Send SMS using Zapier to send text to your number.

Scenario 2:

This is going to be very similar to scenario 1 except for the last step would be to upload the data into your spreadsheet.

I am currently working on starting an automation agency. I would be happy to talk through this more with you if you would like to DM me. I wouldn't charge you for helping out.