1) That charger should work well with our AGM battery.
2) It should be fine, if you have enough room in the building, I'd pull it forward and backward a couple times to make sure the drivetrain stays well lubricated and to prevent flat spots on the tires from developing.
Obviously if you have a nice weather day, I'd take the car out for a short drive. (Also be sure to check for rodents and other animal debris, and hope they haven't chewed on anything.)
2019 Insight EX, Aegean Blue (Owned by my someday wife)
General Automotive knowledge, Degree in Autobody, worked in Electronics for the past 10 years.
Retired Professional Car Audio Competitor. Avid knowledge buff, always researching something.