I thought that the reflexive "esquecer" required the preposition "de" - "vou me esquecer de você"
esquecer requieres de in the presente, like gostar de or precisar de. vou esquecer is another form.
Apenas se vier antecedido de pronomes como (ME, TE, SE, NOS, VOS) Dois exemplos básicos.
Eu nunca ME esqueço DE você
Eu nunca esqueço você
"Shall" is becoming rarer and rarer in English. It's hanging out with "whom".
As used in the above sentence, yes. It is still used, however, to make suggestions/offers in the first person - singular and plural.
Shall we go now? /// Shall I open the window?
I am a native speaker of English and I sometimes say, I never will forget you, with emphasis on never. One doesn't have occasion to say this very often.