My daughter (state primary) definitely had ‘school’ in a weekly spelling list in either year 1 or 2. She was also able to spell ‘pyramid’ and ‘cylinder’ in year 2, but not year 1. I can’t remember whether they were in a spelling list, but they came up over and over again in maths, so she might have learned them that way. I am pretty sure that ‘science’ has not been in a spelling list yet, but again, it comes up a lot, and she knew how to spell it.
She’s now year 3. I’ve just asked her, and she can spell ‘thistle’, ‘glisten’ and ‘enormous’. They have definitely not been in a spelling list. I could see ‘glisten’ and ‘enormous’ coming up in comprehension or in a writing assignment, but was surprised she knew ‘thistle’.
Your spelling list looks a bit disparate. There are 2 words of ‘s as st’ and 2 words of ‘i as y’. Although science and school both begin ‘sc’, they are very different, and then ‘enormous’ is out there by itself.
In our school, in year 1 and 2 they consisted of 7 words following the same rule or two alternative spellings (e.g. -ey and -y) plus 3 exception words, so it was more obvious what they were trying to teach them.