I have the single bank one in my cargo trailer, the light on it stays red while it is charging and then turns green when it is fully charged. It switches over from it’s charging program (which is pretty involved) over to a maintainer.
It should be able to stay plugged in with no problem.
Yep you can leave it plugged in and connected it will automatically switch to a maintenance charge.
However best practice is to switch it off after it switches to the green light.
I have mine on a 7 day plug in timert as soon as I get home I plug in the charger until the LEDs are green. Then it gies over to timed and then on Thursday evenings it comes on for 6 hours to give a top off charge to the batteries so everything is ready to roll on Friday so I can prep the boat after work and be ready to roll Saturday morning, without having to mess with the charger.
The added benefit of the 7 day timer is when I am kept off the water for a week or two, the batteries get a top up maintenance charge every week, which keeps them in great shape.