But I always thought that the last noun determined the gender of the "noun train."
However, in this example, "trinke" and "gerne" have nothing to do with the masculinity or femininity of the juice: "Trinke" is simply the first person singular of "trinken" and, on "gern," the extra "e" is optional.
However, had there been an article in front of "Bananensaft," it would have had to reflect the accusative "den" or "einen."
No. According to responses/comments I read from other users on this forum and also from the link I gave below there is no difference. Gerne is the regular form and gern is just a colloquial variation.