Learn Italian: Mi piace il bricolage; in altre parole, amo creare le cose. - I like DIY; in other words, I love creating things.

Yes, they are highly interchangeable here. In altre parole literally means "in other words" and is used to rephrase something for clarity. You could just as easily use ovvero (meaning "or rather" or "that is") or vale a dire (meaning "that is to say") to connect these two clauses, as all three serve to explain or simplify the first statement.

Is the French word "bricolage" the standard way to say "DIY" in Italian?

Yes, il bricolage is an extremely common loanword in Italy for home improvement, crafts, and DIY hobbies, and it retains a French-sounding pronunciation. Another very common, native alternative you will hear is il fai da te (literally "the do-it-yourself").

Why is the definite article "le" used in "creare le cose" if it just means "creating things" in general?

In English, we usually drop the article when talking about a plural noun in a broad, general sense (like "creating things"). Italian, however, generally requires the definite article when talking about broad categories, general concepts, or abstract ideas. Therefore, "things in general" must be le cose.

Why does the sentence switch from "mi piace" to "amo"?