We study the behavior of vortex matter in artificial flow channels confined by pinned vortices in the channel edges (CEs). The critical current $J_s$ is governed by the interaction with static vortices in the CEs. We study structural changes associated with (in)commensurability between the channel width $w$ and the natural row spacing $b_0$, and their effect on $J_s$. The behavior depends crucially on the presence of disorder in the CE arrays. For ordered CEs, maxima in $J_s$ occur at matching $w=nb_0$ ($n$ integer), while for $w eq nb_0$ defects along the CEs cause a vanishing $J_s$. For weak CE disorder, the sharp peaks in $J_s$ at $w=nb_0$ become smeared via nucleation and pinning of defects. The corresponding quasi-1D $n$ row configurations can be described by a (disordered)sine-Gordon model. For larger disorder and $wsimeq nb_0$, $J_s$ levels at $sim 30 %$ of the ideal lattice strength $J_s^0$. Around half filling ($w/b_0 simeq npm 1/2$), disorder causes new features, namely {it misaligned} defects and coexistence of $n$ and $n pm 1$ rows in the channel. This causes a {it maximum} in $J_s$ around mismatch, while $J_s$ smoothly decreases towards matching due to annealing of the misaligned regions. We study the evolution of static and dynamic structures on changing $w/b_0$, the relation between modulations of $J_s$ and transverse fluctuations and dynamic ordering of the arrays. The numerical results at strong disorder show good qualitative agreement with recent mode-locking experiments.
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