Prize Giving Ceremonies - Teachers Decide or What?

It varies. Effort and attainment prizes are based on grades on their reports. Prizes for kindness are voted for by their classmates or sometimes nominated by teachers. Subject specific prizes are discussed by subject teachers about who deserves it and why.

Different schools will do things differently.
Our school seemed to have 2 types, one for the best academically, and one for the most progress or similar. Then also some random ones such as 'overcoming adversity'.
Some schools will bother to ensure a spread others will just determine per subject which might end up with the same few scooping a number of awards.

Years back my DB one an essay prize in his A level year. It was a bit embarrassing as he had only entered 'for fun' and was doing science A levels.

It will vary from school to school. Sometimes it's based on results, often it's based on teacher nominations. Sometimes a bit of both. Departments may put their heads together and look at results and also attitude, achievement in class etc.

Just a parent here - I didn’t go to a school which had prizes but dh did and my dc’s prep school does.
So far I would say our prep gives the prize to the pupil who has the highest achievement ( taking into account the whole year) in that subject that year. Sometimes they award joint prizes to two pupils.
Not giving an opinion of if this is right/wrong/other, just seems to be how it is done and how other parents feel it is done.

My dc never win anything - unsurprisingly the prize winners become fairly predictable year after year! I wouldn’t worry about it in the slightest.