Perhaps you can have the Esbit stove (check the rules!), but fuel of any sort is definitely no-no for carry-on. After you arrive at your destination, perhaps you can head to an outdoor shop and get a Mora and some fuel tablets.

The ziplock bag is a great idea.

You should be able to take on board with you a knife-less multitool. I recommend that you open all the tools like an octopus for inspection. You may still have to explain there is no knife and thus is permissible.

Also, check the local law at your destination about carrying a knife.

I'm very sorry for your loss.