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I have BIGOTS for 15ac I got within Bs. Can't see it being BAGOTS.

15 is fine! Nikki meant 13 - she posted very quickly to say so (at the same time I was posting my bewilderment!).

I suppose I'd go for the K spelling as it contains ASK but half the time I solve these with no idea how I've done it as the wordplay is often so obscure.

So have I, Filmfan.
(R = rook = take + ask, all backwards).

And by the same token 4 down is TAROK and not TAROT as it's T (initial letter of Trick) ,then A and then ROCK (danger) minus the C for caught.

I agree!

16a is a tease. I thought I had a sensible answer to the cryptic part but can't find the resulting word in Chambers. I may have the wrong container. Any HINTS, please.

This might not be much help.
I had the last four letters of the answer - and just worked my way through Chambers. It took only a few minutes to come across a word which is defined as 'the jiggery palm' - so that seemed to fit the second part of the clue. I still don't know how the first part works.

If others without the paper would like to help(with a HINT), here is the clue...
Usual empty container up front is source of brown sugar (5)

Sorry, 'jiggery palm' should have been 'jiggery palm'.

Thanks Malone. Still can't understand the first part of the clue either.