my son has not been offered a place in any of the schools requested

Some places do put you on the list automatically, some don't.
The appeals process is more on personal circumstances It really isn't for reception places. It needs to be an error on the council's part or a serious problem to win an appeal because of infant class sizes.

You should look into appealing in order to get into one of your three preferred schools. School places are usually allocated by 1) siblings and 2) distance. The appeals process is more on personal circumstances. Schools can be instructed to take additional children even if they are technically full. You might be able to speak to the schools in order to establish which one you're most likely to get into. Probably the closest one I would guess, as proximity would help with making your case.

Whatever you do, don’t reject the place you’ve been offered. If you do that, you can be given any place left in literally any school in the srea.
Did you have a reasonable chance of a place at the schools you put down?

Did you put your catchment school on the list?

You will need to sign up to the continued interest lists for the schools on your list, you won't automatically be put on them.

Accept the offered place.
The council won't sort the waiting lists out properly for a couple of weeks yet but once they do they should be able to tell you where you are on the list.

You need to look at other schools and check up where you are are on the waiting list. You also need to see if you have grounds to appeal the decision. But be prepared for the three chosen schools not to have spaces so a plan b is essential.

You might want to get this moved to Primary Education topic. For year 1 entry it would be an In
Year application which you would make in a year or so's time. However Infant Class Size restrictions mean you would only get a place then in an oversubscribed school if a child left and there was no waiting list or your child met the usual admissions criteria higher than those on a waiting list. You can ask the allocated school to defer your dc starting until he has turned 5 , as long as that is no later than Easter, in the hope you got a waiting list place elsewhere in the meantime.

No, you don't go through the process again (Jan 2020 deadline) for year 1 - that's reception only.

Your son does not need to be in school by the time he is 5. He needs to be educated but that can be home education.

In our area school nursery have already made offers of places and most will be full.

The first thing I would do is phone the three schools you wanted and find out where your son is on the waiting list - I think they can tell you this. This will give you a good idea of how likely he is to get a place by Sept. People do drop out (eg move house, go to private school) so the lists do move a bit.

Your child needs to be in school by the time he's 5. I don't think you can just decide to keep him in nursery for reception. The nursery may not even accept him.

If you apply for year 1 the same schools will be full if there is a waiting list already. You should accept the place you have been allocated and wait it out lists for any school you would accept. When is your dc 5 as legally you can delay entry until the term afterwards. Whether a nursery will keep him from September though is up to them.