I tried translating "Grandpa fell down the stairs and got serious injuries". Since "Grandpa" is the subject, I used the particle は (wa), and since the action is in past tense, I used the ~た (ta) ending for 落ちる (ochiru):
After checking my translation attempt, the correction showed おじちゃんが (ojiichan ga) and 落ちて (ochite):
I know that the particle が (ga) is used for existence of the subject or to express desire, but I don't need to express existence here. Why is が used instead of は?
As regards ~て (te), I know that the ending ~て (te) is used for progressive and imperative tenses, but again I don't need them here. Why is ~て used instead of ~た?
Since I am a beginner in Japanese, I cannot tell if I'm right or wrong. Can someone explain it to me?