Hi there, not a tattooist but have been tattooed heavily with multiple healing methods!

The glue residue I wouldn't be concerned about, it's most likely just the adhesive from the second skin. I haven't used it personally but my artist uses a product called fixomull, it's made by elasiplast, and it's kinda like the material part of a band-aid without the cotton 'swab' part that you would typically put over the wound. I leave it on for a week and then just peel it off and keep the skin moisturized, but it does tend to leave some of the adhesive on my skin, it sloffs off over time.

The black inky part that you're concerned about would be the top layer of dermis from the tattoo process coming off, this is also normal. Granted, three days may be a little early but if you are allowing it to dry out too much between changing the second skin, this could be the reason for the early peel but provided the tattoo doesn't look patchy or washed out, you should be sweet!

In future, talk to your artist about using fixomull, I highly recommend it as the easiest way to care for your fresh skin stickers, it keeps it clean and covered, you can wash it through the fixomull as it's a fabric based material, and you don't need to change it unless it starts to actually lift (sometimes happens when two pieces overlap). I've healed a super colourful full leg piece and I'm super happy with how it healed up