What's the meaning of the word 'legit' in the following sentences:
1- He's a legit person.
2- That's a legit question.
It seems to me to be some kind of AME slang, but I can't find anything in dictionaries, but something related to law.

Thanks in advance for you time to answer my question. :)

Question

What's the meaning of the word 'legit' in the following sentences:
1- He's a legit person. 
2- That's a legit question.
It seems to me to be some kind of AME slang, but I can't find anything in dictionaries, but something related to law.

Thanks in advance for you time to answer my question. :)

Answer

I don't know what AME means, but you are right that legit is used as a slang word. It means "real", "trustworthy" or "accepted".

Answer

I'm 44 years old and the word "legit" was being used before I was born. i would encourage you if you haven't already to get a urban dictionary. You will find a lot of slang words and idioms that you often here from many urban youths...well, actually all hear frequently in American speech.

Answer

"Legit" is short for "legitimate" which means "valid" or "within the law/rules". In both your examples, you could use the full word "legitimate" and it would sound fine.  Using "legit" sounds very casual. It's fairly recent (maybe ~20 year old) slang.

Another example: 
A: "A guy I met on the street downtown said he'd sell me an iPhone for $50."
B: [sarcastically] "Sounds legit."

Answer

Raquel, realmente esses são exemplos de linguaguem casual, jovial até. No segundo exemplo, quer dizer que é uma pergunta que a pessoa que fez realmente quer saber a resposta (não é uma pergunta irônica ou retórica). No primeiro, quer dizer que a pessoa realmente é quem ela diz ser (não uma pessoa se passando por outra).  Quer dizer então "legítimo", "verdadeiro", "fidedigno", "genuíno". 
Pronuncia-se leGIT (palavra oxítona).

Answer

It means 100% sure