Learn Portuguese (Portugal): Este é o hotel mais antigo do mundo.

In Portuguese, adjectives usually come after the noun they describe. To say something is "the most [adjective]", you generally keep that normal word order: o [noun] mais [adjective]. So, "the oldest hotel" translates to o hotel mais antigo (literally "the hotel most old").

The English translation says "in the world", but the Portuguese uses do mundo (of the world). Why?

When saying that something is "the most" or "the least" within a specific group, place, or category, Portuguese uses the preposition de (of) rather than em (in). Since mundo is a masculine noun, de + o combines into do. This is why you must say do mundo instead of no mundo.

Could I use mais velho instead of mais antigo to say "oldest"?

You could, but antigo sounds much better here. For buildings, institutions, or things with historical value, antigo (ancient/old) is the standard choice. Velho is generally used for people or for objects that are physically worn out and broken.

Why does the sentence start with Este and not Isto?