Process guidance for new development team leader
I suspect I'm late to the party, but I've survived a few similar scenarios and might have some tips for you.  It sounds like your team has been over-managed and has grown hostile to process or rules in general.


Do not go directly to Agile and sprint based development.  Consider going with Kanban, and link work items to an epic/larger context.  Sometimes that context will be "break/fix" and sometimes it will be features.  Linking will help you make it clearer where time is spent.  Kanban is preferable because it's likely the absolute minimum process necessary to get work done - it won't require you to bludgeon your team with buzzwords, burndowns, estimates, and other distractions.  It WILL allow you to limit the amount of work in progress - I suggest you start with 3-4 things per team member and try to whittle it down until you can reach a state of continous flow.  Lead your standup using this kanban board.  
Look for opportunities to incentivize smaller delivery batches, and run them through an automated testing process.  Use this process to gradually improve the code base and build trust with the release managers who currently introduce friction to your delivery process, which causes an increase in change/batch size, which causes increased risks, which "validates" the need for an outside gate to production.  
Break up monolithic repositories, then break up monolithic applications.  Smaller applications again mean smaller batch sizes and reduced risk.  
LISTEN a lot.  Your team has been traumatized by a toxic manager, and you have damaged goods on your hands.  If you come in too hot, you'll break trust.  ESPECIALLY through the early phases of this transition, building trust and rapport are the keys to you ever getting a devops practice off the ground.  
DO NOT switch tools simply because other people, who seem to be better at this than your team, are using them.  Do I think there are better workflows than your team has?  You bet!  But don't switch for superstitious or personal reasons.  Understand WHAT your current toolchain prevents you from achieving and make sure that the underlying concepts are understood by every single member of your team before you begin.  
Be prepared for this to take a year or two to really turn around.  You will need to apply slow, predictable, steady pressure on the organization in order to drive meaningful or longterm change.