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?
I think you're wrong because we have "yaşındayım" in another sentence. If "ı" were possessive, it should be "yaşımdayım" instead.
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.
Sara, i have the same question and looked for an answer in different sites of turkish grammar. I have found that in https://turkishexplained.com/nouns.htm. If i understand well, "yetmis yasinda" are indefinite compound nouns= "his 70th age" "yas"+ "i" possessive siffix + "n" buffer before "da" locative suffix. Why "yetmis" without genitive suffix? They give this example: "araba kapısı"= "car door" as indefinite compound nouns and "arabanın kapıları"= "the car's door" as definite compound nouns. . What do you think about that?