Is jedzenie the nominative case? Because I notice that with lubic' the noun often declines.
I think that for some types of nouns, the nominative is the same as the accusative.
Depends on the context. Most probably it's "People here like food, I also like food", so "Ja też/także lubię jedzenie!", but if for example you just mentioned that you like airplanes and now you want to say that apart from airplanes you also like food, that's "(Ja) lubię też jedzenie!"
Do "lubie" and "lubię" have the same pronunciation?, how can I differentiate them?
Well, actually "lubie" is not a word.
But it's quite common that the 1st person singular and 3rd person singular form only differ by ę/e, true. And frankly, most Polish people would probably pronounce them the same then, so you only know it from context.
ę is nasalized e, but if it's the final sound of the word, it's usually just pronounced like e.