First, well done on an excellent set of grades! Hopefully I can help in terms of the ones you are less pleased about.
So, at present and in general, the submitted estimated grade can't be appealed....However, there is an exception to this rule where it is suspected that the school has made an administrative error. They need to contact the SQA - details for this in the spoiler...
On applications of maths, the lack of evidence means you're not in a great situation (and the papers you have done now won't be considered, as the cut off for evidence being generated is 29th May). Speak to your school to see if there is anything at all they can use as a basis of an appeal (they surely must have used something as the basis of the estimate!).
About the impact...Do not worry about the applications of maths qualification - generally people do not have both this and maths, and universities/colleges will
not look less favourably on you for it being a D. They are looking at what you have that does meet the requirements, rather than what doesn't. You don't need straight As to get into uni
For a bit of perspective, I've never seen a uni course that needs an A in Nat 5 maths, and overall, your Nat 5 results are less important than your highers when it comes to applying to uni. I can totally understand it's frustrating to not get the grades you were working at throughout the year, it doesn't make a lot of sense, and we've seen that the system isn't very fair, which is why I'd definitely encourage you to appeal...But don't forget, you've achieved a fantastic set of Nat 5 grades, and I'm pretty sure that those results haven't shut off any options for you!
Hope this helps