I guess it depends on whose definition you use; Norwegian papers at the time quoted experts (presumably a professor of international law, though I can’t remember) who claimed that legally speaking, having troops in uniform venturing into another country counted as an invasion.

Considering all the notes being passed back and forth afterwards, the conscripts must be kicking themselves for not keeping quiet about it; they weren’t observed by Finnish border guards; rather, they notified their officers when returning to base that they’d crossed the border; the army notified the DoD, which notified the Foreign Department, which notified the Finns, who said ‘Huh?’

That depends on each countries' laws.

No, it doesn't.