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Originally Posted by mbs
...so for instance the 7th chord of Eb is Eb-G-Bb-C.
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Oh, mbs, I'm afraid you're on the wrong track altogether. The 7th chord of Eb is D half diminished (or dmin7(b5). That is D-F-Ab-C. Or, if you mean a 7th chord built on Eb it is Eb.G-Bb-Db. Or if you mean an EbMajor seven, it's Eb-G-Bb-D. Regardless of what you mean you're wrong on all accounts. The chord you spelled is an EbMaj6 or just Eb6 chord.
mbs, none of us was born with an understanding of theory and it just takes time, so you're not the only one. However, before you start worrying about composing I suggest you get a'hold of a good theory book or have someone explain more theory to you. You won't be able to grasp composing until you have a good grasp of at least basic theory.
Regarding your question on the composing process, composing can be completely melodic, with the harmonies a consequence of melody. Or someone can take an existing harmonic progression and write a melody to it. Or a combination, where the harmonies and melodies gradually evolve together.
The short answer to your question about the purpose of harmonies is, traditionally, to give forward motion to the composition. This motion can be interrupted or even static and in post-Classical composition the harmonies can be used simply to give color.