Can I use a 12 speed crankset with 11 speed cassette?

Yes, as long as the crankset is designed for the same or more speeds than the chain and cassette it all just works fine.

Yes.

You need to use a Shimano 12S chain on a 12S Shimano ring. The 12S chain works fine with 11S cassettes.

(the tooth profile is different on the rings compared to normal narrow/wide. Not sure about SRAM 12S rings...)

I've used a M7100 crankset with a United cinch ring and an 11 speed chain on a boosted 148mm frame with no issues.

With Shimano cranks you'll need to decide on 52mm or 55mm chainline. Technically with a 148mm frame you'll run 55mm boost cranks but 52mm non boost cranks work fine.

Shimano "boost" the cranks (axle length) not the chainring (like SRAM).
The main benefit of this is tyre / frame clearance.
The boosted axle is longer and uses two 3mm spacers.

7100: 52mm chainline & 172mm Q factor
7120: 55mm chainline & 178mm Q factor

(the tooth profile is different on the rings compared to normal narrow/wide. Not sure about SRAM 12S rings…)

Works fine on sram with an 11s chain.

I've been running Eagle chain rings on an otherwise 11s setup for a few years.

As JonEdwards says - while you may get away with an 11 spd chain on a 12spd Shimano ring, the chain retention will be affected. The chain/chainring profile on Shimano 12 spd is different from 11 spd.

I've got 12 spd XT chainset with a 12 spd XTR chain on an 11 spd Sram GX cassette and a GRX 11 spd mech - been bang on.

Yes, it'll be fine but with caveats. Make sure you get the M7100 crankset which has a 52mm chainline.

I've got SLX M7100 crank set with a 10 speed MTB setup & 10 speed chain, and it works fine. Narrow/wide chainring together with clutch on derailleur and I've never had the chain come off, admittedly I don't ride aggressively.

The differences on Shimano 12 speed are that the chain has slightly longer internal plates and the 12 speed chainring, derailleur & cassettes are designed to accommodate the 12 speed specific chain. So, using a 10 speed chain like I'm doing means the 10 speed chain doesn't fit the chainring perfectly possibly causing premature wear. Using a 12-speed chain on a 10/11 speed cassette/derailleur means that the chain is bit too tight on the cassette/derailleur, again possibly causing premature wear.

On as side note, using a 12 speed Shimano chain on a worn 10/11 speed drivetrain might be good idea as the extended internal plates will fit better on a worn drivetrain.

Not seen any wear on my cassette from the chain.

Not seen any wear on my cassette from the chain.

That's good to hear. Probably, initially there's a bit of wear on the chain and cassette and and then the two fit together perfectly. 12 speed chain on a 10/11 drivetrain is probably better than the 10 speed chain on 12 speed chainring like I have got, the internal chain dimensions will always be too big for the chainring.

You might run into issues with the 11sp chain not meshing well with the shimano 12sp chainring.
I couldnt get a shimano 12sp chain to work well with a shimano 11sp chainring. Never tried the other way around. Shimano's 12sp chainring and chain profile is significantly different to 11sp and earlier.

Also, one persons "works flawlessly" is another persons "works well enough". Depends on what you're willing to put up with regarding shifting performance and noise.

You might run into issues with the 11sp chain not meshing well with the shimano 12sp chainring.
I couldnt get a shimano 12sp chain to work well with a shimano 11sp chainring. Never tried the other way around.

The other way around works fine.

12 Speed XT Crank and Chainring.

11 Speed SLX Casette.

11 Speed SLX Chain.

Works spot on. No Chain retention issues. Quiet.

Before changing to 12s I ran an 11s SLX cassette and 11s chain with SLX 12s chainset on my hardtail for about 15 months with no problems at all.
it was quiet, meshing was no concern and there was no excessive, unexpected wear.

I’m running a Luddite 10speed set up on a 12speed chainring. Works perfectly.

You need to use a Shimano 12S chain on a 12S Shimano ring. The 12S chain works fine with 11S cassettes.

I've been using a 12spd xtr chainring with an 11spd xt chain and 11 spd e thirteen cassette for well over a year now, never once dropped a chain, had zero issues with shifting and had no excessive noise or wear. Recently fitted a 12 spd slx crank to a mates bike, 11spd slx cassette and chain and he reckons it's the smoothest shifting he's ever known so I'd have to disagree on the above

Seems fair to accept Shimano's recommendation re 12 spd chainring and chain given that they differ from most with the extended inner chain plates and correspondingly shaped teeth, but the cassette sprockets don't appear to matter (on the GX cassette at least) as they don't contact the extended plates as far as I can see - there's no marking on the black coating for example, and no feeling of friction/rumbling.

The chain/chainring profile on Shimano 12 spd is different from 11 spd.

How does this work when chainrings are just advertised as Narrow Wide ? Nothing said aboyt SRAM or Shimano specific.

Shimano's 12 spd MTB rings are for HG+ only.

Aftermarket rings from others are offered in different profiles for different chains if done properly.

AB:-

https://absoluteblack.cc/shop/shop/mtb-oval-chainrings

One Up state this to be compatible with most chains but not Shimano HG+

https://uk.oneupcomponents.com/collections/chainrings-1/products/xt-m8000-chainrings

Just because something hasn't yet been a problem, doesn't mean it won't be. The cost of tooling up and making specific rings is worthwhile from a litigious POV given the risk of someone being injured from a dropped chain.

ou need to use a Shimano 12S chain on a 12S Shimano ring

you don't - been running a 12sp XT crank and chain ring with an 11sp chain for ages with no problems what so ever.

I’ve been running the Deore 11 speed group with the 12 speed crank for 18 months.
The deore chain ring wore out first. Replaced with an SLX 12 speed which is lasting better.
Only issue is the stupid little T15H bolts. I’ve lost 2 so far.