Do visual cortical signals always go back and forth between the thalamus, or other subcortical structures, or can they travel directly from one region in the cortex to another?
Intracortical projections can be routed directly to other cortical areas (cortico-cortical projections), or via the thalamus (cortico-thalamo-cortical projections).
Intracortical projections do not have to cross the thalamus or other subcortical structures. Take for example the visual system - it features many cortical projections and these connections do not always enter the thalamus or other subcortical structures (Fig. 1). These connections are called cortico-cortical projections (e.g., Guandalani, 1998). Connections going via the thalamus, however, also exist in the visual cortex (e.g., Kato, 1990) and are referred generally to as cortico-thalamo-cortical projections.
Fig. 1. Visual system. source: McGill
The projections from the LGN to primary cortex (V1 in Fig. 1) and via V2, V3, V4 up to V5 all may occur without visual information entering the thalamus or other subcortical structures.
Also note that on the cellular scale direct cortico-cortical connections in the cortex are abundant (Fig. 2).
Fig. 2. Local cellular connections in the visual cortex. source: Kang et al. (2014)