watasi no otouto ha kuruma wo unten dekimasu ga, watasi ha mada unten dekimasen.

できます is the potential form of する when it follows a noun or noun‐like verb (a “suru‐verb”). In this sentence, 運転 is a noun that normally takes する (運転する = “to drive”), and the potential form of する is できる, meaning “can do.” So 運転できます literally means “(I) can do driving,” i.e. “(I) can drive.”

For nouns that pair with する, Japanese expresses their potential simply by attaching できる to the noun. Instead of saying 運転することができます, you can shorten it to 運転できます. Both are correct, but the shorter form is very common in everyday speech.

• Regular ru-verbs: drop -る and add -られる (e.g. 食べる → 食べられる).
• Regular u-verbs: change the final u sound to the corresponding e sound and add る (e.g. 書く → 書ける, 行く → 行ける).
• する and suru-verbs (noun + する): replace する with できる (e.g. 勉強する → 勉強できる, 運転する → 運転できる).

Here, は marks 弟 as the topic of the sentence (“As for my younger brother…”). 私の弟 is understood from context (the preceding 私の), so adding が to mark the subject is unnecessary. Using は emphasizes the contrast later introduced with 私はまだ…できません.

This が is a conjunction meaning “but” or “however.” It connects the first clause (弟は車を運転できます) with the contrasting second clause (私はまだ運転できません).

を marks 車 as the direct object of the verb 運転できます. In Japanese, the thing being acted upon (the car being driven) takes を.

まだ means “still” or “not yet.” In まだ運転できません, it indicates that up to now you have not learned or gained the skill to drive, but there may be an expectation that you will in the future.

Yes. Japanese often drops subjects when they are clear from context. After mentioning 弟は… and contrasting 私は once, the second 私は can be omitted in casual speech: まだ運転できません. However, including 私は makes the contrast very explicit.