Yes but 3 phase is slightly different and the phases are different pulse widths.
As previously mentioned, that is complete and utter rubbish. Unless you had some timing reference, then if I offered you one phase out fo the three, then there is zero chance you could tell me which phase it was, or whether it came from a 3 phase or single phase supply.
Easy to correct on a small motor by simply swapping two of the phase wires over, but on some of the big stuff I regularly worked upon - you checked the phase rotation and made sure the motor went the right way first off, because they were so difficult to change heavy cables over.
At a previous job, we got a couple of large (for us) water chiller units installed for office AC. We knew that the site had reverse rotation, so every install had to have two wired swapped somewhere. The manufacturer's engineer came to commission the units when they'd been connected - so it was a quick prod of the armature on each contactor and see which way the fans ran, or whether the compressor units "rattled" in a manner characteristic of that type, and swapping two wires round as needed. Turned out that of the 6 motors (3 fans, 3 compressors), one was reversed compared to the rest
If the current rating on both ends is the same and the supplies have a neutral (I suspect they do, but you should verify) I see no problem with making up a lead with a 3 phase plug and a single phase socket.
Neither do I
Leads with different current ratings at both ends are more dubious (though commonly constructed in practice).
Indeed. A socket with a lower current rating than the plug being an issue in terms of circuit protection.
A higher rating socket than plug might not be an issue - depends on situation. I've been thinking of exactly that - fitting a 32A plug on a welder so that where a 32A socket is available it can be "cranked up", but where a 32A socket isn't available then use a 16A or 13A socket and dial back the current accordingly.
You can't do anything DIY in a commercial premises.
Rubbish. What you can't do "legally" is anything you aren't competent to do - which has little to do with being "professional" or "DIY". After all, on here and other forums there are plenty of examples of supposedly "professional" work which is anything but.
And being pedantic, anything done in-house is DIY - the in-house person did it (DI) and it was him that did it (i.e. Y, yourself). Also, if he's being paid then he is a professional - i.e. is being paid to do something.
provided you have complied with all of the required directives in designing and assembling it, tested it properly and completed the declaration of conformity (which you will obviously be keeping available for at least 10 years) and marked it appropriately with UKCA or CE or both marks depending on where it is to be used.
Riiiight. So when you get a professional electrician in to make up an adapter lead, he'll do all that will he ? Err, I doubt it.
On the market = the thing exists in the UK/EU and can be used in a commercial activity.
Wrong, it does not mean that. The legislation you link to is clear in that :
"For the purposes of this Directive, the following definitions shall apply:
(1) ‘making available on the market’ means any supply of electrical equipment for distribution, consumption or use on the Union market in the course of a commercial activity, whether in return for payment or free of charge;"
Note the "supply of ...". If I make a (in this case) cable for my own use, then this is not a "supply of electrical equipment" and therefore it has not been placed on the market. It's more interesting if I (or the OP) get in a sparky to make one for me - and may depend on how the contract is worded.
It could be argued that if I say "I need a cable to do ...", the sparky goes off to the wholesalers for the bits, and comes back to me with a cable to do <something> then that sparky has placed the cable on the market - but I doubt many would be saying that it would be reasonable (assuming he used all appropriately marked components) to expect him to go through the full declaration of conformity malarky.
On the other hand, if I got the parts and employed the sparky on an hourly rate to assemble them for me - then there's no doubt (except perhaps in your mind) that nothing has been put on the market.