Learn German: Ich baue ein Häuschen, um das Bäumchen zu schützen. - I am building a little house in order to protect the little tree.

Any noun that ends in the diminutive suffix -chen (meaning "little") automatically becomes neuter. For example, even though "tree" is masculine (der Baum), the diminutive "little tree" must be neuter (das Bäumchen).

Why do Haus and Baum change to Häuschen and Bäumchen? Why do they get umlauts?

When you add -chen to a noun to make it smaller or cuter, the root vowel almost always takes an umlaut if it is an A, O, or U. Here, the "au" in Haus and Baum changes to "äu" in Häuschen and Bäumchen.

How does the um ... zu structure work in this sentence?

The combination of um and zu translates to "in order to" and expresses the purpose or goal of an action. Here, um das Bäumchen zu schützen means "in order to protect the little tree."

Why is schützen placed at the very end of the sentence?

In an um ... zu clause, the main verb always stays in its infinitive (dictionary) form and gets pushed to the very end of the clause. The word zu sits right in front of it to complete the "to protect" meaning.