Learn Dutch: Zullen we de brief morgen sturen? - Shall we send the letter tomorrow?

This is a classic example of the verb bracket. When you use a modal verb like zullen (shall), it takes the normal verb spot, and pushes the main action verb (sturen) all the way to the end of the sentence.

Why does the sentence start with Zullen instead of we?

Because this is a yes/no question. In Dutch, to turn a statement like we zullen (we shall) into a question, you swap the subject and the verb. So, the conjugated verb comes first: Zullen we...?

Is Zullen we the standard way to make a suggestion?

Yes! Just like in English, asking Zullen we...? (Shall we...?) is the most common way to suggest doing something together in Dutch.

Could I put morgen before de brief?

It is better not to. In Dutch, a specific, definite object like de brief (the letter) almost always comes before a time word like morgen (tomorrow).