I read that when attempting to sell a first manuscript, you need to send the full manuscript to agencies/agents, and not just a query letter.
Also, is it okay to send the manuscript to another agency after after a few months, or even at the same time? I’ve read that you should, and that you shouldn’t. It seems to me that because it’s exceptionally hard to get a first book published, and because most manuscripts are rejected, that it’d be best to send them to multiple places. On the other hand, I read that agencies hate this. Which is it?
First of all, I don't know where you read that, but you should send a query letter first unless you read on the agent's website to do otherwise. Don't go wildly sending out your manuscript unsolicited. It's expensive and it won't get you anywhere. In fact, it will probably annoy us.
You are permitted to send material to multiple agencies at the same time. In fact, we pretty much assume you're doing it and that all submissions are simultaneous submissions unless the query is from someone who knows the agent personally. If you're blind-querying us, we assume you're blind-querying at least 10 other people at the same time. When I used to work in a building with five agencies in one complex, we would get the mail in a big pile and the interns would sort it, and we would often see the same letters quite obviously going to every agency there on the same day, because the font would be the same or the envelope would be the same. If you're going to query multiple agents at the same address, at least have the decency to spread it out by a couple of days and give the appearance that you care about us specifically.