I'm really not convinced this is a real-life situation but I'm going to give it a shot!
Tufguy, your post was messy, awkward and overly wordy. Is that really what you would write in your own language if you were writing this letter? I very much doubt that it is. I have assumed that the writer has already been offered a position at the company. This is what I would write:
Dear Mr/Mrs/Miss/Ms [surname]
Thank you for offering me the position of XXX at [name of company].
I understand that the position involves working five days per week. Could you clarify if those working days are always Monday to Friday or is there scope for taking days off during the week? Also, I would be interested to know if it is possible to work a six-day week.
Thank you and I look forward to hearing from you.
Yours sincerely
[your name]
If this is a general enquiry being made before applying for a job (or before being offered a position), I would write:
Dear Sir/Madam or Mr/Mrs/Miss/Ms [surname]
I am interested in working for your company. However, before I apply for the position of [job being advertised], I would appreciate it if you would clarify the situation with regard to the working schedule. Do employees work Monday to Friday every week or is there scope for flexibility in the schedule?
I look forward to hearing from you.
Yours sincerely
[your name]