"Μερικοί" is just some without indication of number whereas "several" emphasizes that there were a lot of people.
Hm, for me at least, "several" is a comparatively small number - "several parents" might be five to nine, or thereabouts, which I wouldn't call "a lot" yet.
Yes, I get your point. Here I think the main idea is the existence of parents in the house and not the number. ;-}
"Some parents are at home" isn't correct but "Some parents are in the home" is?
That's right. The best translation for μέσα στο σπίτι is "in the house", though, rather than "in the home".
"at home" would mean their home but here "house" could refer to any house since there is no context. "At my friend's party the children played in the garden and the parents were in the house."
Yes, I'd say so. 'Some' is vague, e.g. 'some are, some aren't', while 'few' is a comment on how many.