Learn Swedish: De är stora och tunga. - They are big and heavy.

Because the subject of the sentence, de (they), is plural! In Swedish, adjectives must match the noun or pronoun they describe. When describing a plural word, you usually add an -a to the end of the adjective. So, stor becomes stora, and tung becomes tunga.

Is de really pronounced the way it is spelled?

Actually, no! Even though it is spelled de, it is almost always pronounced like the word dom in everyday spoken Swedish. You will only hear it pronounced exactly as written in very formal situations or on the news.

Could I use dem here instead of de?

No, because de is the subject pronoun (they), while dem is the object pronoun (them). Just like in English, you say 'They are big,' not 'Them are big.' However, in spoken Swedish, both de and dem are usually pronounced dom, which is why they are so easy to mix up when writing!

I have heard native speakers change the word och when talking. How is it pronounced here?

You have a good ear! In everyday speech, the conjunction och (and) is almost always shortened and pronounced simply as 'å'. So you will likely hear this entire sentence spoken as 'Dom är stora å tunga.'