what is best way to rip Neo-Geo bios logo sprites from other games as a raw binary GFX data?

maybe you will find some helpful information here: eyecatcher-image-using-datlib

And why eyecatcher melody in my game fading out so sharply at the end?

opposite to the logo this sound is not coming from the bios and is played by the game itself. most games do this via FM, the NGFX-driver uses a short ADPCM-sample for this, which may not be perfect or optimal but is very small and saves space in the V-ROM.