I can answer some of the questions:
During the past year, responses from Will Shortz have come between two and three months after I've submitted a puzzle--usually closer to two. That applies to both responses where the puzzles are politely declined and where they're accepted. I've always received a reply, sometimes from Will directly and sometimes from his assistant, Paula Gamache.
I'd agree that there is some useful information missing from the specification sheets of multiple publications. I sent a rebus puzzle to the LA Times and only discovered after receiving a response that they never run rebuses.
I haven't heard an official statement about concurrent submissions of the same puzzle to multiple editors. I've avoided it thus far, figuring that I'd rather wait a little longer to have a puzzle accepted by a second editor after an initial rejection than bother any of the editors by doing something that could at least irritate them. I don't imagine it wouldn't bother any of them to be asked about their feelings on the topic, though.
Best of luck on the puzzles you've submitted.