Don't rely on just looking for glue marks as you can easily miss them. Wet the wood with methylated spirit, turpentine or white spirit (nasty smelly stuff but cheaper than turps) and you'll see the lighter spots where the glue prevents the liquid from soaking into the wood. It's not always 100% effective, but better than just using your eyes on the dry wood.

Some of that should come off with sanding. Some of that binding is quite proud of the body so you'll probably want to level it off anyway.

Otherwise the normal recommendation is Goof-Off, an acetone based glue remover. Or you can use pure acetone (the extra ingredients in Goof-Off make it a better glue remover but acetone should work). You'll need to work it into the wood, ideally with a small soft brass-bristled brush (Amazon/eBay/auto stores). But mask off the binding first as acetone will first mark and then dissolve the binding if left on too long. But you can always fine sand and polish the binding for any small marks made during cleaning.

Acetone can be used to stick binding to the wood and you can dissolve binding in acetone to make up a mixture for filling small gaps between binding and the body.

Acrylic ink is basically a thinner form of acrylic paint. I've no idea how well it will mix with stain/dye, though I'm pretty sure it would have to be a water based stain. All I can say is try it out first on some scrap wood. You may need to get pure tinting compound/pigment rather than a stain for best results.

You then need to be careful with the type of clear coat you put over the top as it can depend on the acrylic ink formulation as to whether even acrylic clear coat will go on top properly without any issues. I've had acrylic sprays look like they've dried, but never hardened fully because they went on top of something they weren't 100% compatible with.

If you experiment, you always put yourself at risk unless you try these things out first, which can add a fair bit of time to the project.