It's okay to use "said" a few times. You don't always have to have an action, or a synonym for "said" attached to every piece of dialogue. Also, if two people are talking, you can just alternate their words, as long as you throw in an action here and there to indicate who's speaking, just to help the reader keep them straight.
Check out Jan's Master Class (or is it Writing Basics?) in the forums on the topic of dialogue. That particular lesson has multiple examples of how to write effective dialogue.
One trick I suggest is to read your piece aloud. Sometimes when you hear it spoken, you can catch the mistakes. Go over it with a fine toothed comb, reading and rereading, observing carefully the punctuation and choice of words. You may need someone with an editorial mind to help you with a few entries just to get used to what's expected and what to look out for.
Your piece has a great message, and ties in nicely with the topic. It's got several grammatical errors, and reads a little choppy (maybe too many scenes), but it's got great potential. If you want a line-by-line critique, let me know. I can carve out a little time to show you what you need to work on.
Keep writing! You can do it.