Some misunderstandings that are making this more difficult than it needs to be.
Suggest reading the FAQ under the stickies.

Can't your trainer see your Fitbit logs - which has your workouts listed and totals of meal calories and macros?

To your points:
1 - that function is if you want to log your sets & reps on MFP - it has nothing to do with calories
Do it on Fitbit as you are. Because indeed, for calories that is more accurate manually logged than by HR-based calorie burn which would be inflated.

2 - when you log Weights under the Exercise database - it would have an estimated calorie burn there already. You can replace it or keep it. It's small compared to cardio and that's true.
But Fitbit is giving a better estimate - so to the point of using their exercise Diary, don't do it on MFP anyway.

Fitbit sends steps as a figure for viewing - that's it's only purpose.
Fitbit sends Total Daily calorie burn to MFP - that's all that is needed to figure out your eating goal.

MFP sends meals to Fitbit.
MFP will send manually logged workouts back to Fitbit to replace what it had.

But if you are getting the calorie burn form Fitbit - you are merely increasing the odds of a mistake, and getting hit by sync issues.

Log your workouts on Fitbit if you did NOT use the device function to log it already.
Log your food on MFP and it will transfer to Fitbit.

Show your coach your Fitbit Food and Exercise diary for their comments.

Know that with Fitbit Activity Records you can log extra info about the workout for notes and such. Just edit it. (MFP has no such ability)

Eat to your MFP goal, which is calculated from Fitbit Total burned less your selected deficit.
As the day goes on there is more math occurring - but that is basically what MFP is attempting to do - correct itself to that Fitbit total.

Ok I know I'm being dense here - I'm a little unsure of what to make of the different information available on the forums. If I have a Fitbit versa (which does measure heart rate) and I do an exercise class that is not step based but does increase heart rate, and I choose to automatically track the exercise while it's happening so it automatically gets recorded in the Fitbit app, should I also add the exercise in MFP, or will the calorie deficit automatically be sent to MFP? Or does the calorie deficit only get calculated based on my step count, which in this case wouldn't take into account the non-step based class I took?

Today for example I did such a class, and I also went over my step count (unrelated). I had a calorie deficit show up in the MFP app. I also added my exercise because I didn't see it transferred over from Fitbit. I've since read that Fitbit doesn't send exercises so that makes sense - and when I recorded the exercise my calorie deficit jumped up to like 800 calories. While I would LOVE that to be the case it just doesn't seem right.

Thank you for explaining it like I'm a child (read: please explain it to me like I'm a child).