I believe before it was called "Bangladesh" it was
East Pakistan.
That is true.
Yes. Civil war broke out, and Bangladesh was carved out of erstwhile Pakistan, by Indian forces in 1971. Bangladesh was initially a secular country, but was soon taken over by an Islamists-supported dictator, who executed the country's founder.
After that, Bangladesh began a spiral into radicalization and violence. The present government there is in cahoots with the Islamists, and is aided by Pakistan's Inter-Services Intelligence (ISI), the group which created and trained the Taliban.