Exam

You can't get actual CAT question papers as it is restricted by IIMs.
However, you can get a similar pattern of questions from various coaching institutes. Books following the previous year's patterns are also available in the market which I think, will suffice your needs.

Yes, you will get admission, if your JEE Mains score is good, otherwise you will get average rated college.

Almost all universities are conducting entrance exam for B.Ed. You can apply in RIE for B.Ed or central university for B.Ed. They are highly demanded as compare to state university B.Ed.