Draw a line under this week - it's gone, you can't change it, but you can learn from it and implement a plan next week to make next week different.
Get yourself a notebook, and start filling it out as you go with the standards and processes. Make yourself a checklist of everything you need to review before you pass somebody a document. Then each time you complete a task refer back to it and check off everything. And definitely start saving templates to use.
If you have time it can also help to set aside a letter, complete another task, and then review it with fresh eyes. If possible, printing a copy for yourself to review off screen, at least while you're getting to grips with it all, can help. I often notice things when it's printed that my eyes skimmed over on screen.
It can also help to read documents backwards to check spelling etc. When you read normally your brain has a tendency to show you what you think you should be seeing so you can miss mistakes. Whereas reading backwards forces it to pay attention to what's actually there.
Lastly, be kinder to yourself. Employers expect new starters to be anxious and make mistakes as they get to grips with things. Panicking and telling yourself you're useless and about to be fired is just feeding the anxiety, which was causing the mistakes in the first place. You're going to get stuck in a vicious circle if you continue.
What would be a kinder and more rationale thing to tell yourself? They've invested in you, see capability in you, and want you to succeed. You're capable of these tasks if only you can slow down and be calmer.
Find a more helpful, believable thought to tell yourself next time you start to panic and then pause, take some slow breaths, and carry on once you're feeling calmer. Reminding yourself you can do this.