Will the shiny and scratched appearance after sanding between coats go away after applying another coat of polyurethane?
The drying times on the can are usually very optimistic in my experience. They sometimes state the drying conditions the times are intended for, like 78 ºF and &lt;20% humidity. If you are colder and/or more humid you will have to wait longer.

Definitely do not sand if the finish is tacky. There's no harm in giving it extra time to dry.

At this point I would wait for the finish to really dry, then sand it again until it is smooth. You may have to take off some/most of the first coat of poly to get a smooth surface. Do NOT just spray another coat onto a sticky, bumpy mess. It will just be preserved like that.

Polyurethane won't smooth out any bumps, that's what the sanding is for. The surface will get more lustrous but it won't get any smoother. If you've prepped the surface well and removed all dust, there won't be any bumps at the end.