Can I publish an ebook that contains information from lots of other books, or is there some publishing law/copyrights law that stops me?

Scholars and scientists cite other publications all the time.  They just make sure that the authors get proper credit within their own texts.

However, if you are planning simply to lift long passages from other books, you might have to seek special permission to do this. Publishers have rights offices that take care of this sort of thing and follow the law when they want to put together an anthology or something similar. You don't.

So, you'd really need to consult an intellectual-property lawyer about your plans.

Making money off other's works, even if you cite them, might make you vulnerable to a legal action.  Write your ebook.  Precisely cite every other work you used. If it actually gets to the point where an author you cite wants money, deal with it then.  

While you're at it why don't you make a film by splicing scenes from existing films together and then call the finished product "your" movie? I don't see any problem with doing that. 

Editorial commentary is covered under the Copyright Law amendments of 1978. That is the place to start insofar as determining your use. Some additional legal precedents have likely been set since. If you intend to publish and are uncertain, you simply need to consult with a qualified copyright law attorney.

Sure just put, "And as reported by Mr. so and so in the whatever"  before the information and then you can play with it, cuss it out or praise it......  

You'll need to contact the owners of the publishing rights for the original books to get their permission, and properly annotate and credit all the relevant information

You cannot just copy sections from other books; that is a breach of copyright.

You can usually use concepts, as long as you describe them in your own words, that do not duplicate the working from other books.

eg. Paraphrasing things.

That also depends on where the idea or concept originated, though. If it's something that has already been included in many books or is general knowledge, it should be fine.

But, something unique and original by one specific author need much more care to ensure you do not violate any rights they may have relating to it; which could result in legal problems.