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I have heard many times in the name of Rabbi Shimshon Rafael Hirsch that every Hebrew shoresh (usually defined with three letters) has a more basic root of two letters. I also heard in his name that letters which are phonetically similar are also interchangeable in shorashim.

Is it true that he said this? If so, where did he say this? Are there any rules for the application of this?

(The concept of two-letter shorashim is not completely foreign to traditional Judaism; for example, the HaKsav VeHaKabalah uses it.)

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(L'havdil, Jastrow was a proponent of the two-letter-root theory.) For "that letters which are phonetically similar are also interchangeable in shorashim", see RSRH's commentary throughout Chumash: he does this over and over and over again. – msh210 Aug 17 '12 at 5:22
I'm no expert in Hirsch, but I'm pretty sure that he uses three-letter roots for Hebrew words. He does however use the idea that each individual letter has an independent general concept associated with it which sheds light on the meaning of the roots with that letter. Also, phonetically similar letters are not interchangeable in the sense that switching one for another results in the same meaning, but rather that words with such "interchangeable" letters have related/similar/comparable meanings. See the introduction to this book for further elaboration. – jake Aug 17 '12 at 6:04
ba, msh210's right R' Hirsch analyzes phonetically-related roots as related (as @jake very aptly rephrases your "interchangeable") very frequently. You needn't dig too far into Sefer Bereishit to find the first example. See his commentary on "Bara" in 1:1 (p. 3 in the earlier English translation), where he compares the root BRA to the roots BRCh, BRH, PRCh, PRA, and PRNg, "which all have the meaning of striving to get out, or getting out a a state of being constrained or bound." – Isaac Moses Aug 21 '12 at 3:59

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