some image editing tools for webdesign

Inkscape already has many of those

* blur & sharpen
Blur and Sharpen effects are available for raster images (at least in development versions) in Effects > Raster
There is also blur filter for vector objects.

*crop
you can use the Clip command (Object > Clip > Set), position the object that has the shape you want over the image and use Clip

*selecting parts and deleting it or separating it
I guess you mean Magic wand tool or similar, Inkscape doesn't have it (AFAIK) but you can work around it by duplicating the image and using Clip to different areas. But I think in this area bitmap editing software is the best choice.

*merging images
Object > Mask > Set, use an object with white to transparent (or black) gradient and place it on top of the image. You can use more than one object to mask, and you can mask only one image or both to get various effects.

*some scripts for brightness and contrast and hue saturation
You have Levels and Contrast under Effects> Raster, I'm not sure if Hue and Saturation can be affected by one of those
You can however change Hue and Saturation of vector objects (Effects > Color)

*slices areas editing
lots of people already use a workaround where they add a new layer for all the slice objects. Align the slices, make them transparent. Lock that layer while working on the actual drawing. When it's time to export turn the slices layer on and export away.

*export as HTML page with slices
Do you mean something like sliced images in a html table? I don't see the point as that's malpractice. As far as I know the editor that converts graphics to html and css doesn't exist, if you want it done right you have to code by hand.
Anyway you can use the actual .svg to display in browser, I just haven't figured out how .svg is related to .html as far as semantics and SEO go. I imagine it can make sense when external css comes into play...

can you please test one of the development builds and report back if it satisfies your requests

Inkscape is specifically a SVG (vector) editing tool, not a raster editor. Even with that, as prkos addressed item by item, effectively everything that you requested can already be achieved in Inkscape (with the exception of HTML pages being generated). If you feel that this is in error, and that the suggestions made by prkos don't fulfill your needs, please feel free to re-open this and tell us what doesn't work for you.