That binding looks like it pulled away from the wood shortly after it was glued - you can see that there's a bit poking out beyond the body. You should be able to get a thin bladed knife in there and cut that couple of inches of binding free, scrape away the old glue and then glue it back in place. Either use superglue (being careful not to get it on the wood below the binding if you want to stain it, or use acetone as a solvent to melt the rear of the binding to stick it in place. Multiple pieces of masking tape will hold the binding to the curve.

The fretboard should go right up to the edge, so the top of the binding should be hidden.

AS Frankie says, those veneer tops are very thin, so do try and steam the dents out. A steam iron on a steam setting with some cotton cloth between it and the veneer should hopefully do the trick.

You could simply stick the old nut back on, but a bone replacement is a cheap and worthwhile upgrade. A smear of PVA or Titebond will do the job. Just clear away the old glue with a flat needle file first so there's a good base to glue it to.

The veneer join line may not be perfect, but it doesn't look too bad in the photo. Other people here have had worse join lines and still carried on with a burst or stain, with a good looking end-result. To get over it, some people have done a reverse burst- with a dark centre and lighter edges. But it is a very personal thing, and only you can decide whether you can live with seeing it each time you pick up the guitar.

Unfortunately you also need to check for glue marks on the veneer. Rub the veneer with a cloth with some turpentine, methylated spirit or white spirit on it (these wont affect the glue holding the veneer on like water can). The veneer will darken but any areas with glue on will stay white. Along the center line and around the edges are the normal locations if there is any glue residue on the top. This needs to be removed before staining, and most commercially available glue removers should do the job. I don't know if you have access to a product called 'Goof Off' - but that's what a lot of people on here have used.

Also note that the US sandpaper grit numbers vary a bit from the grit numbers of the sandpapers used in Australia and the UK - above 320 grit the US grits are finer. Comparison chart here: https://www.thesandpaperman.com.au/a...ion-chart.html
Also note that Micro-Mesh grit sizes (Micro Mesh is great for polishing finishes) are also different.

Hope you can work through your problems and get to enjoy your build.