Esbit tablet in planes

For a definitive answer, you should contact the airline

Me thinks it will not be allowed, both in check-in luggage or hand luggage.

One internet reference : https://www.lonelyplanet.com/thorntree/forums/europe-scandinavia-the-nordics/norway/esbit-solid-fuel-tablets-in-check-in-luggage

And Eurowings own documents:

https://www.eurowings.com/en/legal-information/general-conditions-of-carriage.html

See items 8.4.1.1.4 Explosives and flammable substances

and

8.4.1.2 Articles prohibited from being placed in hold luggage.

1. In the US it is specifically forbidden by law. EU air travel regulations forbid it under 'inflammable items. Air safety/security

2. & 3. In the US if you knowingly do so you will be fined heavily. The above linked page does not have information on what they will do if they catch you.

Normally when I intend to cook with esbit on a trip that includes air travel, I plan on finding it locally after arriving. If it is questionable to find in a specific location, I look at other fuel options or go with no-cook meals.

Esbit tablets are made of hexamine, which is an ingredient used in the manufacture of the explosive HMTD. HMTD, like its cousin acetone peroxide, is often used in improvised explosives by terrorist groups. It's also easy to detect even in small quantities by the chemical sniffers used at airport security screening. Best not to try bringing it on board.

As the other answers have pointed out, it is illegal to bring it on board. I will answer the part what would happen if you brought it with you.

Obviously, I would never even dare to think about bringing something I know to be illegal on board. So I have this from a good friend who has a habit of taking Esbit tablets with him in the plane.

After taking Esbit tablets on a plane dozens of times (now probably in triple digits), most of them in hand luggage (usually within Europe) and in a minority of cases in hold luggage (usually from Europe to/from another continent) it only has been detected twice. In hand luggage we are talking about 1-3 packs, while in hold it can be up to 6-7 packs.

What happened in the two cases that it has been detected? The first time was in Manchester a few years ago. The packs of tablets were stored in the cooking pot. Security took a look at the packs, saw the inflammable logo on the pack and took it out saying that you can't bring inflammable goods on a plane. Since that encounter the Esbit packs were always stored in a side pocket well away from cooking gear to make it less obvious that it is part of the cooking gear.

The second time was last October in Brussels. At that time security went straight for the Esbit packs and took a closer look. It was clear that the scanner had identified them as a suspect part of the luggage that needed closer inspection. After studying the packs for a few minutes he put them back in and surprisingly allowed the Esbit packs through, but I wouldn't count on being that lucky.

So to answer your questions 2 and 3: they will usually not be detected (I know nothing about Düsseldorf, but in Glasgow they stayed undetected) especially if you store them away from your cooking stuff to make the link less obvious. When detected and considered unacceptable they will just be taken away from you without much fuzz.