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Denso 6DOF Industrial Robot Flip vs NonFlip

To flip the wrist on a 6 axis robot, rotate joint 4 by 180 degrees. Rotate joint 6 by 180 degrees in the opposite direction. Move joint 5 to mirror of it previous position, that is if joint 5 was at +...
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No mutually perpendicular line between z-axes, are there still valid D-H Parameters?

Given two linearly independent (read: not parallel) vectors, you can always find a vector which is perpendicular to both of them using the cross product: https://en.wikipedia.org/wiki/Cross_product.
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No mutually perpendicular line between z-axes, are there still valid D-H Parameters?

Absolutely. Depending on which version of D-H you are using, look at the $d$ and $r$ terms to accommodate the offsets.
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