Learn Portuguese (Portugal): O cão da mulher é bonito.

In Portuguese, you don't use an apostrophe-S for possession. Instead, you say 'the dog of the woman'. The word for 'of' is de. Because mulher (woman) is a feminine noun, it uses the article a (the). When you combine de + a, they merge into the contraction da (of the).

Since the owner is a woman, why is the word for beautiful (bonito) in the masculine form?

Adjectives must match the noun they are actually describing, not the person who owns it. Here, bonito describes the dog (o cão), which is a masculine noun. If we were describing a female cat (a gata), it would be bonita, regardless of who owns her.

What is the little wave mark over the letter 'a' in cão?

That mark is called a tilde. In Portuguese, it tells you to make a nasal sound, meaning you push some of the air out through your nose when saying the vowel.

Why do we use é for 'is' instead of está?

The word é comes from the verb ser, which is used to talk about permanent or lasting characteristics. Since being a beautiful dog is treated as a natural, permanent trait rather than just a temporary condition, we use é.