The sentence should actually be read in this way: 按 下面的 顺序 排列。 下 is with 面的 not with 按。 按 is short for 按照。 hope it helps：）

按 means press (verb) also called 按 (verb press ) 鈕 (none- button) - 按鈕 ( none) means button because we press button is called 按鈕 in a direct translation. 按顺序排列 to make it in order is different from Chinese. Do you know News report usually says Press ( urging) in order. To try and persuade some one to do something in order (顺序排列) tightly . 整理 means arrangement 整理(arrangemnet) 一下 ( about a short time), to arrange it for a short time. 放 ( put) 下 (down) to put it down 放 it 下 in a place or 放下 it.

Actually, you have this confusion just becasue you have an incorrect punctuation. The correct punctuation is "按 下面的 顺序 排列 " But "按下" would have different means in different contexts. For instance, "请帮我按下电梯（Please help me to push the elevator’s button）”, this sentence is a abbreviation of “请 你 帮我 按 一下 电梯的 按钮 ”. But in this sentence "他 按下了 按钮”, "按下"is a whole word, "了“ means the verb（按）is finished. As you known, there is no tense in Chinese, so the different positions of "了" in sentence would make differents tenses. It's very complex. By the way, may I have a language exchange with you? I'm studying IELTS, and I want to improve my writing and speaking.

按equals 按照。 按照下面，，，。 i think you can understand 按照 。