Custom Image Code - Need Security

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I'm working on some custom image code, not unlike the [img] tag.

What is the best way to ensure that:
a) the url starts with http:// (not https://)
b) the filetype is .jpg, .gif or .png
c) the url contains no spaces, <, >, ?, $, &, [, ], html, or other symbols that could be harmful
d) the url only contains letters, numbers, /, and .
e) if possible, information on how to check to see that the image is a valid image file
f) not required, but information on how to implement dimension checking would be useful too

If anyone could assist me with the best way of doing these, it would be much appreciated.