In my opinion both are correct on oral speech. In a formal text, you must use Eu a/o vi (it depends if you're talking to a female or male person)

In Speaking Brazilian Portuguese (that includes informal writting language such as e-mail, blog, etc.), the most common is "eu te vi". The formal grammar don't consider correct because, "te" is the same as "tu" (second person) and in Brazil, we use "voce" (3th person). That means, in writing language, we must write "eu o/a vi". But that sentence relly looks formal. So, sometimes we choose "eu vi voce" instead.

There is no diffence, same meaning, but if you use "eu te vi" you need to mention the 2nd person as "tu" for example "Eu te vi ontem, onde tu fostes?"

"eu vi você" "eu vi ele" "eu vi ela" are grammatically incorrect, the correct is "eu te vi" "eu o vi", but we use both to speak.

I'd say: "eu te vi" "eu o vi" "eu a vi" = PORTUGAL "eu vi você" "eu vi ele" "eu vi ela" = BRASIL We have the same grammar in Brazil and Portugal, but in real life, brazilians dont speak like the formal grammar.