You ask a really interesting set of questions - some thoughts:
1) no process/ checklist system in the world will ensure you never make mistakes. You always will, it's part of the process and not something to shy away from. In terms of more practical advice for minimising errors of this sort, I think the best approach is just to be careful and deliberate the first time round, and proof read where you can. It's almost impossible to be 100% correct 100% of the time, though, so I would really encourage managing your expectations to avoid then being too harsh on yourself when errors do happen.
2) I can't speak for your firm in particular, but most firms will use some form of workload management system and you'll also have access to a digital calendar - I would encourage you to use everything you're given access to, but, by the same token, don't overcomplicate what you don't need to. The firm will equip you with all the workload/ workflow management tools that you'll ever need, just focus on getting to grips with that and keeping it nice and simple.
3) You'll get used to it. I know that's infuriating advice to hear, and I also know that it's not terribly helpful to give, but it's the truth. It will be tough at first, but you'll adapt and learn to deal with it. Your system will naturally get used to the pressure/ atmosphere and respond accordingly. I think the quickest route to success in this regard, though, is just not getting in your own head about it. People know you need time to learn and grow, don't overthink it.
Very best of luck with your role!
