The English proverb "You can't have your cake and eat it" is apparently equivalent to the Russian one "И рыбку съесть, и в воду не лезть". What's the exact meaning of the proverb "И рыбку съесть, и в воду не лезть"? How do Russian people interpret and use it (and in which circumstances)? Is it often or rarely used?
Literally "и рыбку съесть, и в воду не лезть" means "eat a fish without getting wet [without going into water]". There are lots of semantic equivalents, some of them vulgar.
One of those vulgar ones has the same first part of the phrase as your example: "и рыбку съесть" -- "to [both] eat a fish" and often is quoted only by the first part (completely appropriate by itself!). So, when you hear someone using that part of the phrase, chances are one's having a rude expression in mind (but often from "high" moral ground, too, i.e. "pointing out the smartarse").
Well, I think that this particular one has more accent on the fact that you get your fish and you haven't done anything to catch that, so sneaky lucky bastard you.
We have a bunch of other possibilities with the same beginning about a fish, which carry "you want too much at the same moment" sense. Note that these phrases below mention completely different activities, on contrast with both your examples with the fish and the cake, which might be essential difference. One of them is that vulgar one mentioned already:
И рыбку съесть и на хуй сесть (to eat a fish and to sit onto a [someones] dick).
The rhyme and the rude word multiply the comic effect of the phrase. Another one which is completely fine for children (well, because children are usually the ones who want too many) would be:
И рыбку съесть и на люстре покататься (to eat a fish and to ride a chandelier).
So in the sense "there would be too many pleasures for you" I'd use (and I do use) the 2 last ones.