Welcome to the community Adrien 
So…displaying a total per day has been suggested a few times (search for Total Spent Per Day to find all of the posts), here’s Hugo’s comment on why it’s not been included in the app so far & a possible solution that’s being worked on -
https://community.monzo.com/t/total-spent-per-day/2643/6?u=alexs
The total per month is available in the Spending tab for both iOS & Android users.
My guess is you’re an Android user? Because there is a Targets feature which enables you to set budgets with the functionality that you’ve described for iOS users.
https://monzo.com/blog/2016/10/03/targets/
It’s on the roadmap for Android users.
Custom Categories have been addressed here -
https://community.monzo.com/t/custom-categories-1/649/14
And discussed in numerous threads since (just search for Custom Categories, to find those), I’m hopeful that subcategories will be the solution that’s implemented eventually to solve the custom categories problem 
but we don’t know whether that’s something Monzo’s working on or if they have a different solution in mind yet…
Yearly Targets would possibly be available once this feature’s released -
https://community.monzo.com/t/targets-custom-timeframes/6242/2?u=alexs
Saving change has been discussed here -
https://community.monzo.com/t/idea-round-up-purchases-and-save-the-change/2164
And you might find the posts on integrations with Moneybox & Chip interesting too.
I would be interested to hear more about what you have in mind for the cash flow reporting though? What would that look like & how would you use that information?
And just to mention, the easiest way to check whether someone else has suggested your idea before, is to take a look at this post -
https://community.monzo.com/t/popular-feature-ideas-bulb-open-wiki/6758/1
It’s generally best to avoid posting the same request twice, as it saves users repeating themselves & the good ideas being missed but it’s no problem if you do post a duplicate by mistake!