Is it possible to set offsets (alignment) for a sprite represented by a PNG image?

Yes, by using utility that you can download Here.

Another question: why is it that there's always a white border around PNG sprites? It appears only in game, images themselves do not have it, for sure.

That's the colour that transparent pixels have. And because of the linear texture filtering they may show up until a specific alpha value is reached. By enabling "blend sprite borders" option you should get less noticeable border.

[quote="Janis Legzdinsh":3ewzkgjo] By enabling "blend sprite borders" option you should get less noticeable border. Actutally this made the border even more noticable. <!-- s:? --><img src="{SMILIES_PATH}/icon_confused.gif" alt=":?" title="Confused" /><!-- s:? -->

Try to use a darker color for the image's background, this way the outline won't be that noticeable, or if you have enough time, remove the most noticeable pixels from the outlines <!-- s:) --><img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" /><!-- s:) -->.

I use transparent background, how I am supposed to "make it darker"? <!-- s:wink: --><img src="{SMILIES_PATH}/icon_wink.gif" alt=":wink:" title="Wink" /><!-- s:wink: --> And I see no sense in removing any pixels because, as I said that border is not on my sprite image, it appears only in game. Sprites have much darker border (drak-red, black).