BCCI will remove Virat Kohli from the post of captain if India fails to qualify for the WTC final. Because they have better options. Rahane has proved his mettle by winning the series against Australia. But I should give Virat Kohli some more time. Although his captaincy has been a bit bad now, still he is a quite successful captain considering the statistics of his entire career.
I don't think so. The BCCI has been very supportive of Virat Kohli until now and he is captaining India ever since 2013 (in test format since 2016). Apart from being the captain, he remains as the most important player in the team, with the Indian batting still overdependent on his form. Under such circumstances, I don't expect BCCI to "remove" Kohli from captaincy. The only possibility, is if he voluntarily resigns from the post. And the chances of something like that happening is very low right now.
You are right. The BCCI is very supportive of Virat Kohli. And that is what should be done. Because Virat has performed the duties of captain so diligently so far. Now he is in somewhat off form. Hopefully, in a few days, he will find out his mistakes. Take appropriate steps to correct his mistakes. And go back to the previous destructive form again