Regulating 12v source to 12v
I don't think you need to regulate the outputs to these devices at all. I have one of these Harbor Freight trickle chargers, is does eventually run the battery terminal voltage up to the 13.2V stated, though with a car battery it can take days to get there if the battery is not initially near full charge. It's only intended for maintaining charge, but your loads are likely low enough that the energy in/out is sufficient to maintain the state of charge.

The regulator in the Uno is a NCP1117ST50T3G per the datasheet for the Uno and will tolerate 20V. This is reflected in the tech specs tab on the Arduino website.

The exact model of the linear actuator doesn't appear on the Firgelli website, but it looks like that's just a brushed DC motor, which will be tolerant of a 10% variation of supply voltage with no issue.