There are some points in this e-mail I am not sure about:
Thank you for your reply. I would like to book the tickets of business class (I think it would be better to say - TO BOOK TWO BUSINESS CLASS TICKETS FOR ABOVEMENTIONED FLIGHT). And I chose (I think - I WOULD ALSO LIKE TO BOOK) the return flight on the 10th of January.
Thank you in advance.
FOR the 10th of January. You don't want to wait until that date to make the purchase, which is how it reads to me.
I also don't like "the abovementioned flight."
Why not just be direct:
Please reserve two business-class tickets on UsingEnglish Airways Flight 1210, with a return on 10 January (preferably in the mid-afternoon) for Isaac Newton and Adam Smith. (I assume you need to provide the names of the people who will be flying.)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
As black and white as that.
Thank you very much indeed.