I hear an 'e' sound between the two n's in "wannie"--is that how it's actually pronounced?
I don't hear it. And no, there shouldn't be anything like that, just a double n, both pronounced.
Does the sound of 'w' before a word starting with 'wa' change the sound at all? I'm finding this difficult to pronounce.
Yeah, it's kinda like double w (knowing this letter as double-u, I guess that would be... quadruple-u? but then again it's a different sound, so double-v...) Anyway, try to pronounce it for a bit longer, it makes more sense then to separate them.
Isn't there a rule that says we need to use ‘we’ before the words starting with ‘w’? So ‘...we wannie’?
No, "w wannie" is perfectly pronouncable, it's just a longer 'w'.
You need "we" when the next word starts with W/F and another consonant.
w Finlandii (in Finland) but we Francji (in France). w Warszawie (in Warsaw) but we Wrocławiu (in Wrocław).