部屋 is a much more common word, so every time I see 部室 I do a double take and have to look again to make sure I read it right.
Grammar helps with those. 大きい is an い-adjective, so it’s used to modify nouns. To change an い-adjective to a noun, you replace い with さ. Hence 大きさ is a noun. You can think of it as going from “big” to “bigness”, but nobody says “bigness” so it’s translated as “size” instead.
大した is a pre-noun adjectival. That basically means it can modify nouns like an い-adjective, but can’t be conjugated or put at the end of a sentence. You’ll still have to memorize the exact meaning, but hopefully knowing that it’s used to modify nouns helps you narrow it down.