To create a vanity address, you will need to tell a program certain criteria that you wish the vanity address to contain and then that program will check various private keys until the public address associated with that private key matches that criteria. In theory a vanity address generator can generate a very complex vanity address on it's first "guess". It would also be possible to create a program that checks for multiple vanity addresses at a time, for example it could check for "BurnAddress" as well as "Burned" at the same time and would save the private keys of any address that contains either of the above words.

It is my understanding that, if you were to assume 100% luck, it takes an exponentially greater amount of computing power for each additional letter in a vanity address, so it would take more then 2x the computing power to generate a vanity address containing 6 letters verses one containing 3 specific letters.

As mentioned in the other thread, it would be very expensive to generate a bitcoin address of that complexity, prohibitively so regarding the amounts of money in question, but this assumes 100% luck.

This depends on the relationship between the private key and the address. If the address is calculated in a different way from the private key then the difficulty to generate an altcoin vanity address could be different from bitcoin.

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It would be my opinion that the best way to handle a burn address when an escrow is being used would be to have the dev of the altcoin to send the funds that are to be burned to an address that the escrow controls, and then the escrow would delete the private key, and since the investors are already trusting the escrow with their money, they should be able to trust hat the escrow actually deletes the private key. Alternatively, the escrow could specify a specific burn address for the dev of an altcoin to send the coins to be burned that the escrow knows is unspendable in order to avoid this kind of dispute, as it is really impossible to know at this point one way or another if the dev did something that does not conform with what is normally done, but is still acting in good faith (and does not control the private key to that address), or if the dev is acting maliciously.

It's a fake address, it is 1 char too long, its just photoshop.

I was not aware that vanity address generator were existing for Bitcoin too. But tell, if it's possible to search address this way, would it be possible to hack an address by entering the complete address as the desired output ? This is something that afraid me, like if someone could generate the same Electrum passphrase as me and stole my coins  ...

So that's nice  ! But are you talking about ? Finding a Bitcoin address' private key or an Electrum passphrase ? Maybe both of them are impossible and I prefer that !

I was talking about a private key, as that was the objective of the thread. As for Electrum, if you're referring to the seed, you need a dictionary attack, I think, but don't quote me on that. It's also a very expensive attack.