First question is easy - deployed is on the battlefield in every sense it could mean.
Second is awkward because various rules have hints about 'on the battlefield' meaning different things. Embarking tells you to remove the unit from the battlefield, when counting the number of units for deep strike purposes, embarked units count as being on the battlefield. Models not on the battlefield by the end of turn three count as destroyed, and noone plays embarked units dying like that. While the rule isn't clear, I would think the sensible option is embarked counts as 'on the battlefield'.