rennet is commonly found in cheese. as for other places, I don't know. rennet-free cheese is available, but you have to check the ingredients.
as for "what is not ok" for vegetarians, vegetarians do not consume any products that require the death of an animal - so meat (and chicken, sealife, etc), rennet, gelatin, carmine/cochineal (made from crushed red beetles, often used as a coloring in foods). those are what I can think of off the top of my head.
it's up to you to decide whether you believe in cutting those things out. if you don't, that's fine, that's your choice, but you wouldn't be vegetarian. if you choose to do those things, great! I prefer to think of "vegetarian" as a word to describe the beliefs you hold, not as a label to try to fit yourself into. I hope that makes sense.
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