Como dizer "Meu querido Umbigo" em inglês

Hi there João,

Literally, this expression in English would be "my dear navel" but if you want an expression that give an idea of egoism you can use "wrapped up in oneself" to refer to someone.

Example:
I hate people who are wrapped up in oneself. (Eu odeio pessoas que são embrulhadas em si mesmo (egoísta).

I hope I've helped!

Perhaps you could say "meu querido umbigo" to the person himsef or to a mutual friend, within earshot, with the intent of being heard. In such case, in English you could also say "Mr. Navel-gazer" as in "here comes Mr. Navel-gazer!" (meaning Mr. Narcisistic -sort of- as well, but in a more colloquial way).

What about "sweet navel O'mine?" can be used?

I never had seen it this way before, so to me it doesn´t sound as a natural way. But let´s wait for more comments on this.