In answer to question 2, children generally have to start school (reception) in the year that they will be 4 on the 31st of August.The only exception to this is that if your child is born between 1st April and 31st August, if you like defer their place to start in the following year.
So for example:
If your 4th birthday is between 1st Sept 2024 and 31st Aug 2025, you will start school in September 2025. If your 4th birthday is between 1st April 2024 and 31st Aug 2025, your parents could chose to start you in September 2026.
In answer to question 3, primary school is from September after the child's 4th birthday to July after their 11th birthday, unless they are born end of July or beginning of August, in which case, unless they have had a deferred start, they will finish primary at 10, but will still be 11 by the time they start secondary.
There could be some flexibility if a child had a disability and has an Education, Health and Care plan, (EHCP) or if the parents decide to home educate, but otherwise that is school.
State nursery will take children between 3-4 in line with the school year. So if the child will be 4 by September 2025, they can join a school nursery in from September 2024. This is not compulsory. You can chose to keep your child in other provision e.g. a 3-4 class in a private day nursery, or with a childminder, or you can simply not put your child in any kind of nursery until they start school.
In terms of your own child, I think it very much depends on how well you feel his needs are currently being met. If you feel he is happy and settled there's no need to move him. Would he settle into the new setting better now than age 4? How much support could the school nursery provide as their SEN funding may differ from the school's? Also remember that attending nursery doesn't guarantee a place at that school, because literally a school nursery can take any child who's parent asks for a space, and can refuse any child if they do not have space. A school has set criteria by which they decide what order to admit pupils.