嗨~Justin!! Let me try this.. so if I set up the levels for those three words that you're confused with. It will be 1.客人 2. 顧客 3. 客戶(from daily life to the real business) . So 客人 is the regular one, also means guest. The level of 顧客 sounds higher than 客人, like if someone calls me 顧客 in a night market I would feel a bit strange, like it's a bit too polite and formal. Therefore, according to that, 客戶 is the most formal one, only use on the real business.
About the VEGETARIAN, there is a shorter one, luckily yes!! Which is "吃素". But you'll have to add a subject before that.
Like 我吃素, 他吃素, 他們吃素, 我們吃素。
So when you come to a restaurant you can ask this: 「請問你們有素食嗎?我吃素」
And they will probably ask you 全素 or 蛋奶素 or 鍋邊素( if you're a vegetarian then you'd know)
Hope it's helpful and solve your concerns.
Happy learning!!
Alvin