How do I get rid of the border around the text box and every image I place
in InDesign?
You've set the default line width to something other than 0. Be sure nothing is selected (click outside *everything*, or choose "Select None" from the Edit menu) and check for a value in the Stroke panel.
Can you preview your work?
Sure. The bottom icons of the toolbar do exactly that: switching between edit mode (you see the pasteboard, guides, frames) and preview mode (you only see your page and possibly selected frames, nothing else). The toggle key is 'W', but be sure you don't accidentally have a text cursor. (The quick check is: press 'W', if nothing happens you'll have a 'w' somewhere in your document.)