Hello @wannabe_artist!
As you have already discovered, you can merge the subtools together in the subtool palette (which will combine the subtools into a single subtool but will not fuse the geometry), and then fuse them with Dynamesh. Or you could use the Dynamesh subtool boolean operations.
The other most common way is to use the Live Boolean feature, to create a new fused mesh in the Tool palette from whatever subtools you make part of the Boolean chain. This has the benefit of working non-destructively (will not alter the original subtools), as well as preserving your topology to a much greater degree, only changing it in areas where the meshes are joined.
Depending on the situation, you may also want to dynamesh the resulting live boolean mesh to quickly generate a surface suitable for sculpting, or to correct problematic topology.