I'm guessing that the full stops full outside the ending quote marks below (BrE style) as exampled because these aren't direct quotes uttered by a person. Am I correct? And do we need commas after 'said' in the first two sentences? I think it slows down natural sentence flow.

Are all five sentences punctuated correctly per British style?

1-The sign said, 'Keep off the grass'.

2-The email said 'There will be a meeting on February 5th at the school auditorium. It is from 1pm to 5.30pm. Please be punctual'.

3-I don't care for his sentence 'It is what it is, so don't worry about anything'.

4-I love the old adage/saying/proverb 'A bird in the hand is worth two in the bush'.

5-She said, 'I love the old saying "A bird in the hand is worth two in the bush".'