which is right?

[var123]

No, thank you. I don't want any more.
No, thank you, I don't want any more.

I am looking at this and I've stared at them so long that both look ok! Anyone?

First is definitely fine. Second fine informally, but if you're writing to a pedant then its second comma should possibly be a... semi colon? Or maybe a colon. Not sure, my brain hasn't woken up yet.

Thanks.

How about?

Yes, please send me these.

Or is it:-

Yes please, send me these.

Or even

Yes, send me these please?

I hate the use of don't want.

It feels SO rude to me. "I wouldn't like any more" sounds far more polite than "I don't want any more". I can't even say the latter without scrunching up my nose and pulling a stroppy teenager face!!

OK.Good point - I 'll keep it polite. Which one should I use though?

No, thank you. I would prefer not to receive any more.

No, thank you, I would prefer not to receive any more.

No, thank you; I would prefer not to receive any more.

1 and 3 are both fine. The second contains a comma splice and while some great authors use them (Kate Atkinson is a fan), anybody even vaguely pedantic would wince.
1 is a little more forceful.

Don't like the middle option.

The first one (with full stop) is fine. It is simply two statements.

The third option is also fine. It links the two statements together more, so sort of explains why you are saying no.

However, I don't think I'd pause between the "No" and the "thank you". I'd just say it as "No thank you".

So I vote for:

No thank you. I'd rather not receive any more.

Shouldn't there be two commas? Therefore technically 2 is right?

Now I'm getting confused about my use of shouldn't.

Why have I lost myself in this corner!!!!

Though I agree smidge has te best option