Be doing that while I do this.
>Do that while I do this. (You need the imperative 'do' not infinitive)
It can be doing that while you cook.
>I can be doing that while you cook.
(Was this a typing error "It"? What/who is "it"? Eg you could say "The washing can be drying while you cook.")
I can devote you more space in the book.
> ( "Can" means "able to" here - is this your intended meaning? Otherwise "could" might be better) "If you want, I could/can devote more space to you in the book"
Thanks for the sending
>Yes perfect. You could also say "thanks for sending the file/spreadsheet/report"
>Shipment -> no, this is something physical e.g 100kg of steel, or a purchase from Amazon.com
>Delivery -> no, sounds physical e.g. a postman delivers a letter
Many thanks (in a formal letter)
> yes perfect
Thanks a lot (in a formal letter)
> No... sounds informal or sarcastic! "Thank you very much" is better e.g. to thank your grandmother for a birthday present. However, I would not use this in business emails.
I give a class about maths.
>Yes. Or you could also say "I give a maths class" or "I teach a maths class". Note: British say "maths", Americans say "math".
I impart a class about maths.
>No. Grammar is good, but no-one would say this. People say "I impart advice" but in other sentences, "impart" sounds too formal or old fashioned
This book is a work of reference in the field of maths.
>This sentence is most correct. But more simple: "a maths reference book" or "a reference book in the field of maths".
This camera is seated on a tripod.
>Makes sense, but "This camera is on a tripod" might be more common
This way of doing that became fashionable in the 90s.
This manner of doing that became fashionable in the 90s.
> Both are fine, but "it" instead of "that" is a little better/clearer. "Manner" sounds a bit more academic/formal than "way", but both words are ok.
The fashion of doing that started in the 90s.
>No, sounds funny (but grammar is fine)