Before answering your queries, I must tell you that recanalisation is not 100% successful. Also, there is a high chance of your having a tubal ectopic pregnancy after this operation (compared to those who do not undergo this surgery). So you must take a calculated decision before going in for this.
During caesarean, the tubal ligation is usually done by modified Pomeroys method (tie and cut) in India. I cannot say about Tamil Nadu. We try and remove not more than 1 cm of the tube. Cost of surgery depends upon doctor and hospital - you are advised to meet the doctor you have chosen and ask him /her. Also, you should be prepared for a conventional recanalisation surgery if laparoscopic method is not feasible due to adhesions etc. (as you have a previous CS).