Please find below for detailed answer
You will have to pay alimony irrespective of number of days she lived with you.
The quantum of alimony also does NOT depend on the number of days she lived with you.
Having answered your questions, I would like to suggest the following:
Since it's a short duration, I would recommend to make up. In a fight/quarrel all abuses are valid. You would have also abused her. So do not mind any of these.
Secondly, making a separate house financially if it is not an issue, then do it. Although I understand that it is your duty to take care of your parents etc., it saves a lot of trouble to them later. Let me give you an example. Suppose you file a Divorce, then she may file a DV or 498A, although it may be be proved that she has filed it with malicious intention, but there are all the chances that she will make your parents a party to the case/complaint. So your parents will have to go to the Police Station and court.
Instead, making a separate house will further weaken her case as she cannot say that your parents ill-treated her, or harrassed her or beat her etc. (Please Note: She can still file false complaint, but effect is very less).
Also, if you make a separate house, court will not ask you as to why did you not go home, etc. I hope you understand what I mean here.
Even before taking legal step, it's better if you handle it yourself. Once your case goes to Police Station or Court, you will have no control over it.
Also, understand that a divorce case go on for at least 3 to 5 years.
Give me a call and I can help you better. Also please do rate the answers, so that we can serve better.