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Totally stuck on an old Times puzzle and don't have the book with me so I can't give myself a few to get me started. Here's one:

"Galileo, for example, is explosive - rebuffing caller" (7)

Looks like HERETIC

High Explosive + citer reversed, though I don't like citer = caller and might therefore be wrong

That's got to be it. I didn't mention it in my first post but I thought the first letter might be H because the clue that runs through it is "Hint for act accepted by dramatist" and I think the answer to that one may be Shadow (do inside Shaw). But as you say about using "citer" for caller, using shadow for hint just seems a bit of a stretch.

Her's another that has me baffled: " Mesmerised girl felt superior to a man". It's 6 letters with B second from the end.

Got me baffled too I'm afraid. Are you sure about the B?

G-ripped perhaps, but I’m not confident.

If it was from the 80s I probably did it in crossword corner (aka "Jurassic Park") in the staff common room, but it rings no bells.
We only did the Times in the staff room, but I much prefer the Guardian.

How about this which would give me a letter running through the one I just mentioned: "Gravely offend local opinion, say"

7 letters and the third letter is C.

I think it's probably a fairly straightforward clue - but I haven't come up with anything.

That’s looks like INCENSE

That looks right. Getting there now.

How about "Gang, and its members" - _ _ N _ I _ S