Well, I don't hold a degree in music or anything, I'm actually a self-taught keyboardist. I never took music classes in college because the music department at my school was more interested in getting you to play the music of a long-dead guy perfectly rather than learning how to write music yourself.
As far as time signatures go, they're very similar, conceptually, to intervals and chords. Rhythm and Melody are two branches of the same concept. If you can understand how chords work (rather than just saying, "Oh, Dmaj, Amaj, Emaj sound good together, I think I'll just play that...") then making the leap to rhythm and time isn't that much more difficult.
As far as modes and all that goes, it's fancy talk. Get yourself a copy of Music Theory Made Easy by David Harp (easily worth eight times more than the eight bucks you'll pay for it). Despite what some may tell you, it is possible to understand this stuff without going into twenty-five hundred years of music history or getting a minor in math.
You don't NEED to know the history of the Aeolian Mode, and you shouldn't want to. Heck, you don't even need to know that all the Aeolian mode is is the Major Scale with a root-key of A, or even that the Aeolian mode exists, for crying out loud. I'm half-convinced that all the hubbub about learning these archaic terms is to further confuse people who might want to understand harmony better.
Yeesh, anyrate, I'll stop ranting now, it's probably not good for me. 
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People who claim the sky is falling obviously aren't aware the earth is falling, too.
