Is it feasible to cover the national curriculum at home?
Meh. You can if you want (very easy to google it and find out what's in it; very easy to download worksheets and activities aimed at teachers). But why would you want to harness your child's learning to something which is aimed at meeting the needs of the average child? Of course that's an efficient way of doing things with a class full of 30 children, but why not instead follow your child's interests and needs? It's just a somewhat arbitrary selection of what one committee thought children of that age should all know - it has an ideology behind it. You almost certainly don't share all parts of that ideology, so why teach it?
My goal is to get DD writing fluently and quickly and work on the creative content of her writing.
Make it not look educational as far as humanly possible. Write shopping lists together. Get her to write treasure hunt clues for her friends. Use writing functionally - if she has a reason to write then it will get more fluent.
As for creative content - maybe that's not her language? Her creativity might come out in imaginative play; in dance; in music; in pictures; in animations. All of that is just as creative - they only concentrate on making people sit quietly and write stories in school because having 30 people crashing around the classroom pretending to be Hannah Montana would be carnage.
Also i want to improve her maths accuracy.
Again, use maths functionally. Just in baking and going shopping. And when she's interested, treasure hunt clues, and finding fun patterns in the world together, and just let it be non-threatening. (paint lots of 7-petalled flowers and label them up with the 7x table - that sort of thing, only at whatever her level is)
Can I really just focus on this for a few months or do I have to do other stuff as well?
You are legally responsible for ensuring that your child receives an education suitable to her age, ability, aptitude and any SEN, at school or otherwise.
You need to focus on whatever is suitable to the three A's (plus SEN if relevant). That might mean a lot of imaginative play; a lot of dancing around the room to crazy music; a lot of walks in the woods where you talk together about what you are hearing or seeing. It almost certainly won't look anything like school - if an education suitable to her a-a-a was going to look like school, you wouldn't be wondering about removing her.
How do I make sure she's keeping up? Do you test children against national levels? If so how?
Personally, I think the best way for someone to learn is for them to learn at their own page and their own stage. They might be way ahead in one area, and way behind their peers in another. But in both areas, they are learning at a level that is appropriate for them. I don't believe life is a race. Just because someone else is learning differential equations at 7 doesn't mean my child is behind or a failure because (s)he isn't.
We don't have to try to look like everyone else once we are HEdding.
Me, I follow the child's interests. We both learn a huge amount from that. Go and read Alan THomas and Harriet Pattison's book how children learn at home. It is life changing!
How much does HE cost?
Everything and nothing. We do all our shopping in charity shops; we don't buy workbooks and things; we have season tickets at the places we like to go, so it's very cheap on a trip-by-trip basis (and the season tickets we have shift as the years go by)
Am I likely to get hassle from the local authority?
Not if you make sure you ask here for bolshy and legally-grounded advice on a regular basis 