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The second row is multiplied by 3, then the third row is subtracted from it. This is equally valid.

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The second part (not returning to base) can be finessed by adding a zero-length arc from every node other than base back to the base node. So wherever you end up last, you return to base at no cost. As for revisiting nodes, if you know in advance how many times each node must be visited, and if there are no time windows or other constraints on when you ...

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As you have noted, this (implicit) feasibility region on $y$ can be formulated as the projection (via $y=cx$) of an explicit feasibility region in $x$. I had to deal with this problem myself recently. One method, as people have commented, is to obtain the vertices from your half-space representation and then project these down; the convex hull of these ...

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