Well, you could have specified that you were talking about "Adam" in a previous sentence and then just use "o" instead of "Adam" which could be confusing.
To me that seems kind of strange. I'm not a native though so if a native could confirm it would be more useful.
I wasn't thinking and put "Adam is seventy years old" for the translation and it still marked it correct :D
This is valid for every word practically. Every word in a language can be used as a proper name in other languages.
If this was a challenge for me I would go with another wording like Adam'ın yaşı yetmiş.
Does "yaş" mean year? Can you explain the structure of "yaşında" to mean "years old"? The -da ending looks locative which makes sense, but how does the -in- fit?
yaş means age. It is literally something like "he is at his 70th age"
I'm not sure, but it could be that yetmiş and yaş are combined in a compound noun, which requires the genitive case suffix -ı on yaş. To imply that someone is of (at) that age would then require the locative case suffix -da, for which the genitive case suffix requires the buffer consonant -n, hence yaşında. But here I'm just combining what I've learned so far, so it could be wrong.