Of course.
What do you mean "Does its tallness account for it?" Height doesn't decrease the need for a brace. It increases it. What is the thickness of the glass? That's a very tall tank to not have a center brace. I'm suspicious that it's not a fish tank, but something more like a terrarium.
You don't. That's what the bio media in your filters is for.
I've filled it with water and let it sit, and it did fine. Around it is actually laminate wood which is pressurized so perhaps it should hold up fine over an extended period of time? Either way I have time to add an aquarium brace, but I am quite sure it is a fish tank because of the lid and how it leaves the exact same spacing for hanging filters and heaters. Also the back has holes in it for power and wires similar to many fish tank stands I've seen (idk if reptile stands typically include them).
The majority of your beneficial bacteria will be in your filter media. The recommendation to rinse the media in tank water instead of tap water is to prevent die off the beneficial bacteria by chlorinated water. So no worries about going bare bottom. Since you plan on going bare bottom, consider extending your filter uptakes to just off the floor. The low uptakes will pick up a lot of debris.
