Is it permissible to take a Tawarruq from a bank that involves a doubtful element (Shubha) in order to repay an amount taken from a trust (Amanah)? And is it permissible to repay it in installments over a long period?

Assaulting a trust is forbidden by Islamic law. You must return what you took whenever you are able, even if in installments. It is not permissible to engage in a forbidden transaction, such as unbridled tawarruq not regulated by Sharia principles, in order to repay a debt; for committing what is unlawful is not permissible except out of necessity.