Yeah, I think that's the point of saying "unironic" instead of a direct antonym like "sincerely" - the latter connotes that the speaker might just be honest or mistaken while the former signals that there's a joke that the speaker isn't in on and that the only acceptable usage of the target term is an ironic one.
Sarcasm is a form of verbal irony, the irony being that there's a difference between what the speaker says and what they actually mean.
Yes, but in this case the speaker is aware of the irony. Unironic just means that there's no irony.
Yeah, I think that's the point of saying "unironic" instead of a direct antonym like "sincerely" - the latter connotes that the speaker might just be honest or mistaken while the former signals that there's a joke that the speaker isn't in on and that the only acceptable usage of the target term is an ironic one.