古いmeans old but its used with non living objects. so What word described people & animals as old
If I Wanted to say my old grandma forgets alot How would I say that.
I know I can't use 古い祖母(ふるいそぼ). I asked my teacher this and she didn't know it. She only taught us 古い.

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I think that my old grandma is ひいおばあちゃん.
ひいおばあちゃん is grandma's mother.

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ancient

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年老いた Toshioita
年とった Toshitotta
These adjectives are generally used for 70~100 years old people. Remember 老 means the target noun is old. If you want to discribe "middle aged", you can say 中年の.