If they want a brief intro, I'd send a paragraph about the story and who it's aimed at (age group) and what other books that audience might like.
If they want a sample, I'd send about 1/5th of the book. Not sure how many pages you have in the book.
I've never written anything for children, so I'm not sure what you mean by marking out each page for the editor. Do you mean marking where the pictures would go? If you do, then I'd say yes, you should do that.
I'd send a paragraph about the story (short synopsis), include the word count and the age group it's aimed at. A sample for a novel is usually the first three chapters so for a picture book I would send it all. I wouldn't put page numbers, I'd break it up by putting it into paragraphs. If you're illustrating it as well as writing it, then I would break it up to make a dummy, using the same lay out as a printed picture book so that they can visualise it. Picture books are usually 32 pages, including the covers and first page so you need to take these into account if you're doing a dummy.
Best of luck Can I be nosy and ask which agent this is please? You can DM me this if you want.