I came up with an answer to my second question (patting self on back right now). The method for re-enabling the Internet Explorer desktop icon can be found in this knowledge base atricle:
Internet Explorer 7 Desktop icon missing. I didn't find it in my original search because it does not list Vista Home Basic in its "applies to" section, but it does indeed work. Those looking for Vista answers in the KB might want to take note, and search for "Windows Vista" rather than a specific edition.