"Yes, in almost all name brands, they carry a childs running shoe in all sizes, including childs size 4.
The size to get for running shoes should be one size less than your regular shoe size. Tighter fitting shoes are best for running.
If you have recently taken up running, and you need to buy some decent running shoes, you can find them at your local Famous Footwear or Payless. Size 14 shoes are pretty popular there for running shoes.
13 is a common size for men so you should be able to find them anywhere running shoes are sold. If the store is sold out, they can typically order it for you or you can order it over the web if not in store.
You subtract 2 to get the size in children's shoe size.
Brooks running shoes are available in all sizes and half sizes. Make sure you know your size when you come into the store that way it cuts your shopping time in half.
Pretty-small-shoes.com is an online shoe shop that specializes in small sizes, or you could try looking in the children's section of your local sports store. Jjbsports.com also carries size 3 running shoes.
Based on the information you have already provided me I would suggest that you buy a size 10 pair of running shoes if that really is your correct shoe size.
Nike does not currently offer the Trail shoe in a children's size. They do offer a similar type shoe.
A website that sells size 10 female running shoes is shoebuy (http://www.shoebuy.com/size-10-womens-running-shoes.htm). They sell a wide variety of female running shoes in a size 10. They also sell a variety of styles and colours.
Sketchers shoes come in many sizes, although it will vary on the style of shoe. There are children sized shoes, and adults shoes up to size Men's 16 US (or 15 UK).
Yes. They do come in size 14.
The most convenient way to find running shoes that are in your size would be to check on a running website such as Road Runner Sports. They will show you what sizes are available.