IIT

Hi,
You can take a coaching in an IIT class but you are not eligible to get admission in NITs and IITs as you have only 60% in boards. You should have at least 75% in your board exams to get admission in an NIT or IIT.

Yes. But please see that the previous years closing rank for B.arch at IIT Kharagpur was 8778.
So, will have yo get a rank accordingly to enter the college.

You are eligible to appear for JEE after Diploma in Engineering to seek admission in IITs.

Which board? If CBSE then your marks are low for IIT, NIT and IIIT. A minimum of 75% required for these for a CBSE board student.

Yes, in order to appear for JEE Mains you need to complete HSC education.

Yes, you can. IITs don't have any interest in the college you opted for UG. They only consider your GATE score.

Please check the college closing rank by JoSAA for IITs and NITs and compare with your rank:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx