The object particle を, the action-place particle で, and inviting/suggesting with ませんか and ましょう.
を (read “o”) marks the thing the action is done to.
まいあさ ジュースを のみます。
I drink juice every morning.
を marks the direct object — what is eaten, drunk, read, etc. The particle を is only ever used for this grammatical role and is pronounced “o”.
で marks where an action happens: レストランで 食べます = “eat at a restaurant”.
レストランで ひるごはんを たべます。
I eat lunch at a restaurant.
で marks the location where an action takes place. (Compare に in lesson 10, which marks where something simply exists.)
V-ませんか invites the listener to do something together: “Won't you …?”
いっしょに きょうとへ いきませんか。
Won't you go to Kyoto with me?
Although it looks like a negative question, V-ませんか is a polite, soft invitation — “shall we / won't you …?”.
V-ましょう proposes doing something together: “Let's …”.
ちょっと やすみましょう。
Let's take a short break.
ましょう expresses “let's”. It is also the natural reply when accepting a ませんか invitation: 行きませんか → ええ、行きましょう.