IIT

http://www.result24.co.in/jee-advanced-cut-off-2015-2016.html
check out this link.
The data almost remains the same over years with minor changes.
And if u get into an IIT but fall between minor branches (beyond Chemical) in old IIT's and CS in new IIT's, opt for CS. It is the future.
All the Best

no they dont give

work hard and practice graphical problems in physics and try to get best conception in calculus part

there is no other way to get admission in IIT. better you should try next time. you may also look for other alternate institutes

Psychology prtogrammes including PhD are offered under the Department of Humanities and Social Sciences at IITs at Kanpur, Mumbai, Roorkee etc. in the areas of Social Psychology, Cross-cultural Psychology, Personality, Indian concepts relevant to Psychology, Cognitive Psychology, Social Cognition, Social Representations of Health and Illness, Military Psychology, Organizational Behavior, Human Processes at Work and Service, including Human Resource Development.

yes, but if you have studied in coaching institutes for two years or you have solved jee books still can't clear jee mains then do not drop a year, many options are there, try wbjee, jcece etc.
BUT if not solved any jee books or not prepared for jee yet, you should first prepare for it then only you will know your capacity. it will also help for future plans which branch to choose. you will go to a college where other students have read jee books so you will have tough competition.