Learn Swedish: Pojken har en söt hund.

Because it describes hund, which is an en-word (you can see the word en right before it!). When an adjective describes a single en-word in its indefinite form (meaning "a dog" instead of "the dog"), it uses its base form, söt. If it were describing an ett-word, it would need a -t at the end.

Is the word order for en söt hund the same as in English?

Yes! Just like in English, the describing word or adjective (söt) goes right between the article (en) and the noun (hund). This pattern is very reliable in Swedish.

Why does the sentence start with pojken instead of just pojke?

Pojke means "boy" in general. To say "the boy", Swedish attaches the definite article to the end of the word. Since pojke is an en-word that already ends in a vowel, we just add -n to make pojken.

Does the verb har change if I want to say "I have" instead of "the boy has"?

No, and that is the great thing about Swedish verbs! Unlike English, which switches between "have" and "has", Swedish uses har for everything in the present tense, no matter who is doing the action.