No. You cannot "mix" statuses. The instant you are granted TN, you must stop working your H1-B job. You would need to get a TN for the original job if you wanted to continue (which employer would probably refuse to attempt).
We have no idea! I doubt it for the TN. For the AP, possibly, but you tried this already. All the rest is poor planning in my opinion. Spouse could have switched to another status to study, and probably gotten OPT for clinical.
1. You are of course eligible to apply for the job. The question is whether it is a civil engineering job, or a management consulting job. You would likely qualify for either.
2. This should not affect your current TN. Remember to secure the second TN and keep the first until you are ready to...
The border is unlikely to accept it, but there is no harm in trying -- UNLESS you have had problems last time with border accepting your quals. -- in which case you might just want to wait to avoid that battle until later.
Your I-94 is good until Feb 2021, and you can continue to work until then. Your TN visa (which is issued at a consulate, is only use for entry into US, and since you have an approved I-129 TN until 2021, your old consular visa is automatically valid for re-entry.
You have nothing to do, and...
Obviously, the officers questioned had no idea, and 1 and 4 pulled the answers out of their ass. Study on TN, TD, H1, H4, etc is considered "incidental" to one's primary status, so is permitted, at any level of education.
It is not a problem, but please explain how your I-94 is 'valid' but your TN 'expired'. Typically if your I-94 and TN expire at same time, or the I-94 becomes invalid before TN expiry. Your situation seems unusual.
So your true start date is October 1, unless your firm decides to have you work outside US, which they can do now.
Yes, you can get TN, and then switch to H1-B when approved. You would need to exit US and re-enter to switch, but since you would be on TN, there would be no rush to do this.
All steps after 6 or 7 require that you are on EAD/AP and no longer on TN. As I said, AC21 does not apply when you are on TN. The entire process outlines still applies, the steps you mention just aren't available to you -because your team didn't ensure you had valid TN for a long enough period.