Yes, whatever gives you your first idea to get started, just start with it. I know a wonderful composer who gets going with whatever sounds happen around him... a bird, a chair falling, a person's voice. What he subsequently writes doesn't imitate those things at all, he's just really interested in sounds and they get his imagination rolling.
Modulation is changing to a different key in the same piece. Sometimes there's a clear point exactly when it happens, like one transitional chord, then boom, you're in F major when you started in C. Other times it takes longer, a few chords or even many many measures. If you fool around with it a little, you'll see that some changes are very straightforward for a composer, like C to F, while others need a longer path to get there gracefully, like C to Ab. Sometimes there's not even a transition, just a hop into the new key. This is dramatic, used a lot in pop music for the "just once more, a little bit higher" final chorus, almost always a mistake in my opinion, but they never ask me.
Modes are scales of different "flavors" or characters. A get-acquainted exercise is to play a C scale up and down. Then play the scale D to D using only the white keys-- keep the notes of the original scale, just change where you start-stop. Then E to E, still on the white keys. Keep going until you've tried starting on every possible note in the C scale. This changes where the half- and whole-steps lie, so each scale feels very different from the others. That's it! You can do this in every key, if you like that sort of thing (I do), just pick a scale and stick to those notes but change where you start.
As you keep studying theory, you'll look a lot at Palestrina and 4-part writing and learn the rules of that. He didn't have those rules, of course, the rules are based on his music. He just wrote what he wrote, and it was so beautiful that composers are still studying what he did almost 500 years later. That's pretty special, but hopefully you won't be intimidated by the rules. It is good to know what great people did because greatness doesn't come along every day, and the standard rules for part-writing teach how to make certain things happen in music: having momentum, a feeling of inevitability, structure, flow... but sometimes you don't want that. Sometimes you want things to feel like they're going backwards or hovering. Hovering or feeling lost can be expressed very well by those forbidden parallel fifths--they are really disorienting, which is why they're forbidden.
Anyway, just play with different scales and forms, and write as much as you can.