Greetings.
For a start, the "unknown" plants are Dracaena sp., probably Dracaena deremensis or Dracaena sp. "Variegatus". They're land plants and I can guarantee 100% that they will die underwater. For some reason they are very commonly sold as aquarium plants. Everyone, myself included, seems to have been stung by this little con trick early on in their fishkeeping career.
So, unless you want to pollute the tank and gum up your filter, take them out and stick them in a pot of soil. They're nice houseplants. But please understand you have no chance whatsoever of them surviving underwater, and taking a "wait and see" approach is basically killing the plants and wasting your money (as well as jeopardising water quality).
Rocks are fine in brackish water aquaria. People have different opinions on what works well. Lava rock seems to discolour the water, even if it doesn't harm the water chemistry. Tufa rock is bright white and I think rather ugly unless covered with algae, but on the plus side it has a (marginally) positive effect on water chemistry by raising the carbonate hardness. I personally like pink and silver granite in brackish water tanks with some nice river sand at the bottom, but granite is heavy and consequently expensive to ship. The seafood counter of your grocery store is one useful place to look: mussel, whelk, oyster and scallop shells can all be used very effectively (once cleaned, obviously). Oyster shells can be cemented together to form big reefs and you can stick these onto bits of stone Small fish like gobies will love these empty shells, and oyster reefs are a very authentic brackish water habitat. Mussels can be used in a similar way, especially when cemented to bogwood in clumps.
I agree with Fella that the use of bogwood is variable. I think it depends on the bogwood; some is better quality (i.e., more decay resistant) than others. You probably get what you pay for. So buying one or two bits of good quality bogwood (such as Mopani wood) may be a better bet than buying cheaper stuff in bulk. But that said, decaying wood doesn't really cause any major problems so long as the water has a reasonably amount of carbonate hardness to neutralise the acids produced. Water changes will help, too.
Do determine which archerfish are for sale in your area; some species are freshwater/low end brackish, while others are low/mid salinity brackish. The low-end species, Toxotes microlepis, is smaller than the other two species, T. jaculatrix and T. chatareus, but not so widely traded. Since all archerfish are potential fish-eaters, choose tankmates with care. The archers in your photograph above appear to be T. microlepis.
Cheers, Neale