I always use a cake leveler to help move the cake from place to place. You can see a post with my tips below
I put it in the fridge the night before serving, and then at room temperature in the mid-morning to thaw completely for an evening event. I don’t have a set time because each cake is different based on size and components. But this is my general go-to thawing method.
Don’t let them over bake, it’s the main reason cakes turn out dry. Know your oven. Does it run hot? If so, reduce your time. Stay close to your oven as the baking time comes to an end. You want a few moist crumbs to come out on a toothpick when you insert it into the center of your cake.
I actually have a whole post on storing, freezing, and transporting your cakes!