What are your suggestions for my daughter's disadvantages of not going to the school I'm appealing for other than distance, local community and friends, the logistics of getting all children to school and nursery on time?
Do not use distance/logistics of getting to school. Transport is not the responsibility of the LA (unless a place is allocated over 2 miles away and no closer place was available). Look at the facilities the preferred school has. The fact that she has no school at all will weigh in your favour. You only have to convince the panel that the advantage of her going to the school outweighs the difficulty it will cause the school to have another pupil. As you are relocating, you could mention that she needs to be part of the local community and make local friendships.
Would my daughter qualify for the fair access protocol? Can it be only on the basis that there are no places anywhere? Also what does a reasonable distance mean, how far is it?
Yes, if your DD hasn't got a school place by 4 weeks, then she qualifies for FAP. It will only be on the basis that there are no places within a reasonable distance. The statutory walking distance for mainstream primary children without disabilities is 2 miles. So if they find you a school within that distance, you'll be responsible for transport. If it's beyond 2 miles, they will provide transport assistance. However, if the LA is going to make a school take an extra child, it makes sense to reduce costs and make it a local school. If they are under the PAN that was set for the year group in year R, it makes even less sense to preserve their numbers.
If we don't win the appeal and it goes to fair access can we still get into the school I'm appealing for even though we didn't win the appeal?
It's a separate process. Tbh, I can't think why you wouldn't win the appeal if the school has 20 less children than they could have admitted in year R. They won't be able to show that they are full. They won't be able to show that the classrooms are overcrowded. It's not very realistic to suggest that a class of 40 next year is reasonable (although legal).
I am worried it goes to fair access and we are given a school that is so far away.
That could happen whether you get a place through FAP or the standard admissions process.
I have another daughter who will be starting next year in reception and I will be applying for her school place this January, if she gets a school near by and my eldest gets a school far away that would be very difficult.
If there is a sibling priority, your DD would go up the list anyway. You may decide that whatever school your older DD is placed in might suit your younger DD. In other words, worry about this later.