了 has two main uses. After a verb it marks a completed action — 我吃了饭 (I ate). At sentence-end it signals a new situation or change of state — 下雨了 (it started raining). The two can overlap in the same sentence.
mistakes
了 does not mean past tense. It marks completion or change, which can happen in the future too — 你到了北京，给我打电话 (when you arrive in Beijing, call me). Habitual past actions take no 了 — 我以前每天跑步 (I used to run every day).
grammar
To negate a completed action use 没(有) and drop the 了 — 我没吃饭 (I didn't eat), NOT 我没吃了饭. 没 already implies non-completion, so 了 becomes redundant.
Top hook is the position-variant of the 乙 Kangxi radical; here it is purely a visual indexing mark. Strict etymology reads 了 as a swaddled child whose limbs are bound, but the modern silhouette uses this single curved stroke as its radical home.
The downward hook closes the shape and historically traces the bound-baby's wrapped legs. As a learning component it functions as a pure positional stroke pinning the radical to the bottom of the square; it carries no independent meaning of its own.
