Thanks Toritoribe.
In #2, of course I am quite familiar with しまう, but in this case I got confused with the combination of 終わらせちゃおう. Using your suggestion like "finish doing", I got things like "Let's finish causing this work to end", which in English is pretty nonsensical, which put me off. Could you help me understand, in a literal sense, exactly how しまおう combines with 終わらせて to create a sensible meaning?