B.Ed

To apply for B.Ed, you should have completed the Bachelor's /Master's degree in sciences, social sciences or /Humanities/Commerce of any other university recognized by University Grants Commission (UGC). For details refer this link: http://www.dypatil.edu/schools/education/b-ed-prospectus/.

Please refer to the link provided below for details regarding admissions in B.Ed. You should be able to download their brochure which contains accurate details regarding fee structure for B.Ed.
https://www.shiksha.com/teaching-education/colleges/b-ed-colleges-india

Teaching is a noble profession and your educational qualifications will help you to seek primary and TGT jobs. You are further advised to do M.Com or MA English to become a PGT teacher in commerce or English subjects respectively.

There are colleges which offer integrated courses in Botany (M.Sc and B.Ed), however, this list of colleges is very limited. Integrated courses in Physics, chemistry, etc., are more popular. However, if you explore online, you should be able to narrow down your search to a college of your choice. For e.g. The Central University of Rajasthan offers integrated courses in Physics and Chemistry (M.Sc+B.Ed).

You can apply for B.Ed after graduating. For applying B.Ed in IGNOU graduation in any stream is mandatory.

Yes Sanjeev, since you have done B.Sc and B.Ed both, you are eligible for CTET and state TETs (of whichever state you are eligible to appear in).
For KVS, you'll be eligible for the post of PGT and PRT teacher, once you qualify the CTET exam.
You can read the eligibility criteria in detail on the following websites:
www.kvsangathan.nic.in
www.ctet.nic.in

Yes after successfully completing B.Ed. you can appear for the Teacher Eligibility Test (TET). B.Ed is necessary these days for a career in the school level teaching job.

Yes, it is a full-time course.
Refer to the link for details: https://www.shiksha.com/teaching-education/course/integrated-b-ed-m-ed-mahatma-gandhi-antarrashtriya-hindi-vishwavidyalaya-wardha-273237.

Yes, you can. You will have to appear for the entrance exam conducted for admission.
You get exact details visit: http://www.ignou.ac.in/ignou/aboutignou/school/soe/programmes/detail/90/2.