I don't know about you, but I really struggle with emails. These sentences were really helpful!
Bit of a tangent, not just emails, not just professionaly, but one thing I find saves me a lot of stress is that I ask less unnecessary questions.
Not: Would you like to join me / go with me and do x? You can't go on day x? What about day y?
Instead: I'm going to do X at date, location, time. If you want you can join me, let me know.
Not: Can you do X?
Instead: I would like you to do X.
Not: When will it be ready?
Instead: I'm assuming it'll be ready by X. Let me know if this is correct.
Not: What's the deadline?
Instead: I can have this done by X. Let me know if this is acceptable.
TLDR: don't ask people permission or assume they won't be ok with what you want to do. Tell them what you're doing/planning/expecting, offer them the opportunity to help/join/give input.
Bonus: makes you come across as less uncertain and saves a lot of back and forth.