Not compatible with Get Image

Can't you just put get_image before image_resize_filter in your input format configuration? Seems like they should work fine together as long as image_resize_filter comes after.

Oh, hmm, you're right it's not a filter at all. Looks like it only works on the Node body field, but I can't see why the two wouldn't work together just fine.

If not, there is any way to force Image Resize to save all external images locally even if they are not resized?

Image Resize Filter already downloads all images even if they aren't resized if enable the Resize external URL option.

But can Image Resize Filter use http://drupal.org/project/imageapi_optimize to all images stored locally? To have better image optimization and page loading.

Perhaps you should ask this question in the ImageAPI Optimize issue queue. I'm not familiar with that module.

But why Image Resize change the path and name of already uploaded by get image images?

Image Resize Filter doesn't know anything about Get Image module or the way it works. Image Resize Filter is simply trying to help organize your files by putting them all in the "resize" directory. It shouldn't cause a negative side-effect on your site though, just empty the "cache_filter" table and all the image locations will be updated as needed.

I empty all caches, but Image Resize really change the url for already uploaded files via Get Image :(

As I said above, Image Resize Filter doesn't know anything about Get Image. Yes the paths will be different because it's Image Resize Filter saving the images instead of Get Image. Image Resize Filter didn't change the path of Get Image images, it saved entirely different images. From what I can tell, you don't need Get Image module at all if you're already using Image Resize Filter.

It doesn't matter if you had Get Image enabled or not, Image Resize Filter would always create the paths under the "resize/" directory and add the dimensions. The path and save location of Image Resize Filter is not configurable.

I don't see why you're having trouble with the path being different, why don't you just disable Get Image and be done with it?

Okay, alternatively why don't you disable Image Resize Filter's ability to resize external images then? It's silly to have two modules that do the same thing on your site.

I feel I've explained this issue enough.