well, that depends on context. while she does not like to sit at home= "ona nie lubi siedzieć w domu" is 100% about her, and her not liking to sit at home.
She does not like sitting at home= "ona nie lubi siedzenia w domu" may also be about her not liking somebody else's sitting at home.
Not much, simply "siedzenie" is a noun so corresponds to "sitting" (which names activity). "Siedzieć" is an infinitive so corresponds to "to sit".
"...sitting home," should not be marked wrong. It doesn't only have to be "sitting at home."
No. Correct in english is... She does not like sitting AT home.. meaning she prefers to be active.
She does not like sitting at home. a very late reply to Trofaste. I think Mrs.Mop's response was meaning that va-dim's answer of 'sitting home' should not have been accepted. The correct English is 'sitting AT home.