Actually,
www.m-w.com gives the following definitions for "advise":
1 a : to give
advice to
: COUNSEL <
advise her to try a drier climate>
b : CAUTION, WARN <
advise them of the consequences>
c : RECOMMEND <
advise prudence>
2 : to give information or notice to
: INFORM <
advise them of their rights>
The meaning of "Please advise" in a business letter conforms best to meaning 2 above, in my opinion. In other words, it can simply mean that you want to be informed of any details regarding the matter. It doesn't necessarily mean that you are asking for counsel or a recommendation, although that could be the communication you receive in response. Given that, I really do think that "please advise" and "please let me know (about this matter)" mean the same thing in a business communication.
I agree that they are not always interchangeable. "Please let me know if you will be able to attend my party on Saturday night" would sound very odd as "Please advise (regarding) your attendance at Saturday night's party". The tone would be too impersonal and formal.
As for Microsoft Word's recommendations, it has been proven time and again that the software is not a reliable test for the acceptability (or unacceptability) of a sentence when it comes to grammar. I would not rely on it at all. For example, I just typed in "I gnu ewe were rite" into Microsoft Word and received no warnings or suggested corrections.
π Smile :)
I'd say that both sentences are requests, not questions, and I would re-word it as "Please advise me as to what I should do." or as two sentences: "Please advise me. What should I do?"