Soft vs hard plywood vs two-by lumber for bed headrest
You can certainly use pine/fir plywood. It depends entirely on the appearance you're after. Pine tends to look more casual or rustic than fine hardwoods. It's also softer on the surface veneer, which is why the best furniture tends to be mahogany, oak, maple, cherry, etc. 

It's not substantially less rigid, though. Hardwood plywood is usually only hardwood on the thin outer veneer. The core of a BC grade pine and hardwood plywood is usually very similar. 3/4" is plenty strong and stiff for your application. There are high-grade plywoods with very thin layers, which makes them more stiff and stable, but that's a different situation than just switching species. 

Whether you can reduce to 1/2" depends on the design. It'll be less flat initially and more likely to warp over time if not supported by a rigid frame structure.