I think your answers are correct. I read an article on gerunds saying that with "would" the verbs prefer, like, hate are usually followed by the to-infinitive. Howoever your sentences I would prefer to eat ....
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yaggy74Here are my observations on a few. I left out the correct ones.
2. I can't be bothered to do my homework. Infinative form - This sounds wrong to my ears!
I can't be bothered - usually is associated with gerund.
5. I would prefer to eat out tonight.Gerund form. "to eat" is infinitive.
6.
dimsumexpress6. Chloe was doing the washing up when I saw her yesterday. Does not use the Gerund form. Not correct, Washing up- is gerund.
'Washing-up' (should have a hyphen) is a noun; it's not a gerund.