Also, can workers retreat unto lakes where mechs are present?
This one would be "No". The Seaworthy ability is for mechs/character only, so while a mech could retreat onto a lake - and carry workers with it - a worker couldn't retreat onto a lake that already had a mech on it. You'd only ever get to do that if you lost combat and you had a mech there able to transport your worker away.
E.g., if you had your character and a handful of workers on the factory and then lost a combat there, your character would be able to retreat to a lake (assuming they had the Seaworthy ability) but the workers would have to retreat all the way back to home base because the character cannot carry them.