That’s because ‘peidio’ takes ‘â’ after it - so ‘paid â siarad i mi’ literally means something like ‘refrain from speaking to me’ (although we’d usually just translate it as ‘don’t speak to me’). You will hear, though, a lot of speakers just dropping the â: ‘paid siarad i mi’ (or even just ‘paid!’)
(I deliberately avoided using paid â with a word that mutates after it, because I didn’t want to enter into that particular world of confusion at this time 
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Dan - I absolutely love it when I hear learners say ‘ah! That’s why it says that on the sign/poster/in the letter…’
It’s like unlocking another door ag allwedd!
Yes ’ Peidiwch yfed â gyrru’ - don’t drink (along) with driving
You’re most welcome to contact me, I’d be delighted to help. 
I don’t blame you for dropping the â after the Paid/Peidiwch command. In fact, I hardly ever say Paid â… Only when I’m talking to someone who speaks in a more ‘formal’ way than I speak naturally, then I change my way of speaking to match theirs. This isn’t a ‘rule’, by the way, it’s just something I’ve observed myself doing a lot!
Yes - you’re absolutely right!
‘Arian’ is silver and ‘Pres’ is brass.
Arian is used to say ‘money’ in South Wales, and ‘Pres’ in North Wales, although nowadays you tend to hear both being said all over Wales due to people moving/re-locating.
This is a guess, and I’m sure there are books out there that will either verify this or tell me how wrong I am, but I’ve always associated the arian/pres thing with there being a copper mining industry in the North and Silver mining in Mid to South Wales.
I bought that book a few months ago, yeah! It’s great!
Oh, I tend to keep the â as I tend to quite formal Welsh anyway (and I love any chance to slip in an aspirate mutation). But I wanted to avoid bringing the mutation into the equation for Dan as I figured it was probably a confusion too far just at the moment. But yes - it’s a very natural thing to drop it.
Unfortunately,I am already very much confused by a lot of the Welsh language and have only just come to understand why there is so many different ways to say ‘Yes and No’ in welsh.
I know - it’s really confusing, isn’t it! I’m of the opinion that the whole yes/no thing should be left well alone until people have got a grip of other stuff (which is what I think SSiW does). I saw some poor students on a ‘blasu’ course (as in, get a taste of what it’s like learning Welsh) having to answer questions with the right ‘ydw’ or ‘oes’ or whatever. And I just thought - well there’s no chance they’ll be coming back for more! I just stuck with shaking or nodding my head for the first year or so…
I found that its easier if you think that there is no yes or no. And that you are answering with ‘I will’ , ‘I do’, ‘I have’ etc. that way I always find the right one to use.
Exactly! It’s quite natural in English to answer the question ‘Are you going out tonight?’ with ‘Yes I am’. So just suppress the ‘Yes’ part and you’re there! 
I think the confusion between â and “a” (and) may lie in the possibility that some Welsh phrases using “â” could be translated (but not literally) using “a” (“and”), e.g “don’t drink and drive”.
I must say, it took me a long time to realise that â and “a” were two different words.
On “arian” vs “pres”: I’ve heard the explanation that it could be because of the relative wealth of the south, being where industry and government was, and so they were used to paying in silver, while the relatively rural north was more used to paying in “brass”, (or copper).
However, that may not have any basis in fact.
I think Dan’s phrase was “Peidiwch ag yfed a gyrru”, so they are both there: “Refrain from drinking and driving” (or, of course, more idiomatically, “Don’t drink and drive”).
On “arian” vs “pres”: I’ve heard the explanation that it could be because of the relative wealth of the south, being where industry and government was, and so they were used to paying in silver, while the relatively rural north was more used to paying in “brass”, (or copper).
However, that may not have any basis in fact.
That is a really clever suggestion, and I don’t care if it has any basis in fact - I like it!
I’ve just realised after posting - if the things you weren’t supposed to do were the other way around, that would read “Peidiwch â gyrru ac yfed”. I don’t know if that helps anyone see the difference? (My apologies if it just confuses things even more!)
Edited to add: I think this a good place to repeat the SSiW mantra: “Peidiwch â phoeni am y peth” - Don’t worry about it! If you really want to know why, then great. But if it all seems too much, just forget about it and carry on - if you use the wrong one, or get it ‘wrong’ no one will know (because ‘a’ and ‘ac’ and ‘ag’ all sound pretty much the same when you’re speaking) and no one will misunderstand you. And if you don’t worry about you’ll continue chatting away, and people will think what a fabulously fluent speaker you are
Yes, absolutely! I encountered this little curiosity last night in one of my Welsh classes. You can say sglodion a sos coch and sglodion â sos coch, and they sound the same to the ear, even though they mean different things. Chips and tomato ketchup is the first, while the second is ‘chips with tomato ketchup’.
Then I started to wonder if there really is that much of a difference between ‘and’ and ‘with’ in the context of food pairings in English.
When we say ‘I want chips and tomato ketchup’ in English, we’re also conveying ‘I want chips with tomato ketchup’. So ‘and’ in English carries this idea of ‘with’, in a very subtle manner.
As @sarapeacock says though, these are not things to worry about when you’re starting to learn Welsh, but it can be intriguing to delve further into the language a bit later on, especially when you start finding all these little curiosities that reflect a nation’s way of viewing the World and its place in it, going back centuries. Welsh can have such a hold on you that it can become a way of life, not just another language to tick off the list. From reading this forum, I get a strong sense that many of you carry Welsh in your hearts despite how much it can drive you up the wall sometimes with its yes and no and mutations and other challenges!