The copper-to-plastic fitting is just a regular slipnut, same as any other drain/trap connection.
On the offset issue... I'll just mention that they're pretty common on sinks, so I don't see a problem. But I'm biased*, so you might want to wait for one of the plumbers to weigh in.
* What, more than anything, strikes fear in the heart of a carpenter? The sight of a plumber walking by with a sawzall in his hand.