男:山口さん、帰らなくていいんですか。6時までに「みなと市民ホール」に行くって言ってたじゃないですか。
女:市民ホールはみなと駅でしたよね。ここからは電車で二つ目ですから、まだ大丈夫ですよ
1)Why is it saying "Is it okay if you don't go home?" 「帰{かえ}らなくていいんですか。」
Yes. It is saying "Don't you have to leave?", "Don't you have to go home?", etc. My assumption here is that this conversation is taking place at the workplace.
2)What does 「ここから電車{でんしゃ}で二{ふた}つ目{め}」 mean?
「二つ目」 in this context means 「二つ目の駅{えき}」 ("the second train station (from here)"). The Hall is only two train stations away from where the conversation is taking place.
For those unfamiliar with this use of 「目{め}」, this Q&A might be of help.
Japanese is an extremely contextual language, I must keep reminding everyone, myself included.