teemo vs evelynn stealth

I believe the interaction with stealthed champions is that they would vision of you if you walked sufficiently close, however you wouldn't have the spotted warning indicator above your head.

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Will stealth break if she walks near/into stealth ?

it wont "break" unless he hits you, but he and the rest of his team can still see you if you are near him. basically think of it as if teemo was an invisible pink ward. eve cant see teemo, but teemo can see eve ONLY IF teemo is in her reveal range. also eve wont get the exclamation mark if teemo is still stealth unless a teammate is nearby, not 100% sure on that one tho since i dont fight against many teemos as eve, but still fairly certain with my knowledge of eve and interactions with other stealth champs.