Doubt you'd be granted a TRV. You could try to move to a neighbouring country and register with the UNHCR. Process takes years, only a small fraction gets resettled and you don't get to choose where you may possibly be resettled.
Anywhere from a week to over 6 months. It’s all case specific. Not being in your home country and applying for a TRV will be an immediate red flag on your application.
