ましょう(-masho)、ましょうか(-mashoka)、ませんか(-masenka)
―ましょう(-masho/-mashou)
This means “Let’s“. “Ashita aimashou.” means “Let’s meet tomorrow.”
―ましょうか(-mashoka/-mashouka)
This is a Yes/No question of “-masho/-mashou”. “Shall we -?” is the closest sentence in English.
Also, this sentence can be What/When/With whom/Where/How questions.
What time shall we meet? → Nanji ni aimashouka.
Where shall we eat at?→ Doko de tabemashouka.
―ませんか(-masenka)
This is a Yes/No question with the negative form of the verb. “Why don’t we -?” is the closest sentence in English. The answer will be Yes or No.
In this sentence, the speaker has to have a specific suggestion/idea, such as
Why don’t we eat sushi? → Sushi wo tabemasenka.
Why don’t we meet at 3? → 3ji ni aimasenka.
That means you cannot make What/When/With whom/Where/How questions with this ―ませんか.
