As others said, the weather throughout Turkey varies significantly at any time of the year.
1) In general rainy, cloudy, cold and windy weather becomes fairly common by November. Freezing weather will be uncommon except in the mountains.
2) The "tourist season" with the highest accommodation rates is certainly over by November. November through March will find the lowest prices in areas with seasonal rates.
3) You would need to be in the mountains of the east for much chance of snow in November but again the weather will be cold in most places .
4) You need at least two weeks for a basic taste of Turkey. During anytime you mention İstanbul alone will take a week for a fair taste. Days in İstanbul will be short and cold (rarely freezing) wet, cloudy, windy weather may cause problems. Even if the weather proves perfect you will have no problem enjoying yourself in the city!!!!!!
5) 5,000 rupees per day per person over two weeks. This does NOT include long-distance transportation--ONLY local.