I was hoping that you could help me put in perspective the custom (or law?) of writing BS"D or B"H (or rather their Hebrew equivalents) on letters or other messages. I am particularly interested in the following aspects: 1) Am I obligated to write BS"D on greetings to fellow Jews, is it praiseworthy, or possibly not at all necessary? 2) When would it NOT be appropriate to write such a greeting? 3) In communication that is meant for non-Jewish audiences, is it inappropriate to use?

It is a custom commonly practiced by many – but only a nice custom; always appropriate and never required. The letters B"H stand for Baruch Hashem or BeEzrat Hashem and BS"D stands for the Aramaic translation of the latter. Some authorities claim the BS"D (as appose to B"H) is an incorrect custom that should not be practiced at all and in Harerei Kedem B 124 Rav Solovaichik notes this is a newly made custom and none of our sages of previous generations ever used that in a letter.