It is perfectly acceptable to send simultaneous submissions (that is, the same manuscript to several publishers at the same time), but it's good manners to mention it in your cover letter. Unless specified, the publisher wants a short cover letter, synopsis (NOT a blurb- a plot outline) and a sample (usually 3 chapters). Check individual guidelines thoroughly.
Age ranges for children's fiction are usually divided thus:
Board books/picture books/easy readers - for toddlers and young children up to about the age of 7 or 8. Usually contain about 1,500- 2,000 words at 32 pages. And obviously contain pictures!
Transition books/chapter books - for ages 7-10. Fewer pictures, more text divided into 3/4-page chapters. Usually around 50-60 pages in length.
Middle grade/junior fiction - for ages 8-12. More complicated themes and sub-plots. 100-150 pages.
Young adult (YA) - for ages 12+. A wide variety of genres and themes. Lengths can be anything from 200-400 pages.
NOTE: Avoid Pegasus Publishers - don't be fooled by their professional-looking website; this outfit is a vanity press in disguise. ie. Although they make no mention of author fees on their website, countless writers report that they are offered contracts which include them having to hand over thousands of pounds. No reputable publisher (or agent) charges fees.
ANDERSEN PRESS - Picture books to YA fiction, up to 75,000 words. Hard copy only. 2-3 month response.
BLOOMSBURY SPARK - Publishes ebooks only. YA fiction 25,000-60,000 words. Email submissions. Will not hear back unless interested.
BUSTER BOOKS - No picture books. Email or postal submissions.
CARINA - Run by Harlequin UK. Publishes ebooks only. Young adult. Any genre and any length. Response 3-4 weeks.
CURIOUS FOX - Ages 8+. No picture books. Email submissions. Will not hear back unless interested.
DAVID FICKLING - Currently closed - check back for submission guidelines.
FAT FOX BOOKS - Ages 3-14. Any genre. Email submissions. Will not hear back unless interested (3 months)
FLEDGLING PRESS - Email submissions. 6 weeks response.
HOT KEY BOOKS - Email full manuscript. 3 months response
INSIDE POCKET - All age ranges. Email submissions.
MOGZILLA - Ages 4-15 (45,000-75,000 words rough guide). Email or post submissions.
MYRMIDON - Currently closed - check back for submission guidelines.
PHOENIX YARD - Ages 3-13. All genres. Email subs only.
STRIDENT - Currently closed, check back later. 7+ to YA. Email a proposal only in the first instance.