As PatriciaHolm says, decisions about admissions will not have been taken by the head on his own. The head may sign the letters but decisions will have been made by the governors or a committee appointed by the governors.
Whilst it is not obligatory for you to complete an SIF in that a school must still consider your application, failing to supply one can affect your chances of getting a place. So, for example, if you apply to a faith school you will not get priority on faith grounds unless you submit an SIF. In this school's case, failure to submit an SIF means you will not get priority for living in catchment. I would imagine the email only went to those parents claiming to live in catchment. For those parents the form was, to all intents and purposes, mandatory. Failure to complete it would result in their child being placed in a lower admissions category.
If you submit an SIF with inaccurate information the school is not obliged to accept any corrections after the closing date for applications. There has to be a line somewhere otherwise parents could submit corrections the day before offers go out and expect the school to rerun the admissions process, which is simply not realistic. As is clear from the SIF, that deadline was 30th November. Any new information submitted after that should be taken into account for the waiting list but not for admissions.
You submitted your correction in February, which was far too late. By that time allocations would have been pretty much final. The school would have returned its list to the LA weeks before you submitted your correction. Given that offers had to go out on 2nd March, there was no way either the school or the LA could rerun the admissions process at that stage. Even if you had submitted the information earlier, if the school had taken it into account they would have been entitled to treat you as a late applicant which means you would only have got a place if they were undersubscribed.
It is true that, if a mistake has been made, the school is supposed to put it right without needing an appeal. However, this rarely happens. Even when there is a clear mistake the admission authority will almost always insist on an appeal. And I'm afraid I don't think the school has made a mistake in your case.
Looking at the SIF, you completed it saying that you still own your previous home and that you moved after 1st September 2016. The school is clear that they will use your previous address in this situation. This is also set out on the SIF itself at the head of the form. So, on the information you submitted, the school was correct to regard you as not living in catchment. And, as you didn't tell them the correct information until February, they were quite right to ignore it for admissions purposes.
You may get lucky at appeal but my view is that you will lose. You made the mistake, not the school. And all the things you complain about show the school acting correctly. Sorry.