"Shall we write?" in Japanese is "書きましょうか?" (Kakimashou ka?) in a more polite form, and "書こうか?" (Kakou ka?) in a less polite or casual form.

"Shall we see?" in Japanese is "見ましょうか?" (Mimashou ka?) in a more polite form and "見ようか?" (Miyou ka?) in a less polite or casual form.

The difference between "電話しましょうか?" and "電話しようか?" lies in the level of politeness.

The choice between them depends on the context and the level of formality you want to convey in your conversation.