Q. When a listing [agent] says they get back to us on queries in X amount of time and on manuscripts in Y amount of time, what does this mean? Unless the listing specifically says no manuscripts without queries first, is it all right to send a manuscript without a query?
A. The first part of your question is pretty simple. It means that if you send in a query for review and they promise to get back to you within six weeks, they will do just that. They will either say "no thanks" or say "Interesting. Send more so I can read it." Manuscripts take longer to review, so an agent's timeframe on that is longer. When writers send in their work, they want to know how soon they will hear back with a yea/nay. This is just an agent's way of answering that for them.
Usually an agent/agency will request exactly what it wants in terms of a submission. If an agent says "Query. Send no mss," then it's obvious that you should query only. However, if an agency says "Query us," that, too, means send a query only. Just because they didn't specifically stop and say not to send a ms doesn't mean they want writers to include it. Simply follow their guidelines to a T.
Even if you disagree with me on this (and I know some of you do) and will send in pages regardless, I highly advise sending only the first five pages, not any more let alone the whole ms. (You are just wasting postage.) And if you're saying, "But my story doesn't get good till page 7! Can't I just send in the first 10 pages?", then you need to go back and rewrite your first chapter so it gets interesting quicker.
But again, do what the agent requests. That's my best advice.