Do Buddhists talk about insides?
I think you must be thinking of 'middle'. Things have beginnings, middles, and ends. And yes the suttas are filled with discussions of all three.

"It was not until I had thoroughly understood the six senses, the origin of the six senses, the satisfaction of the six senses, the problem with the six senses, the end of the six senses, and the way to the end of the six senses, that I knew of myself that I had attained the highest attaining."

Buddhism also discusses 'inside' vs. 'outside' or 'internal' vs. 'external' which is more easily understood as 'personal' vs. 'impersonal'; subjective versus objective.