Die deur is wyd.

• Die = the
• deur = door
• is = is
• wyd = wide

So the structure is very close to English: The door is wide.

Die is the normal definite article in Afrikaans, meaning the.

A useful thing for English speakers is that Afrikaans does not have different words for the based on gender, like some other European languages do. So you use die for all nouns:

• die man = the man
• die vrou = the woman
• die kind = the child
• die deur = the door

Because here wyd is being used as a predicate adjective: it comes after the verb is and describes the subject.

This is the same basic pattern as in English:

• The door is wide.
• Die deur is wyd.

If you put the adjective before the noun, you get a different structure:

• die wye deur = the wide door

So:

• Die deur is wyd. = the door is wide
• Die wye deur = the wide door

That is because Afrikaans adjectives often change form depending on where they appear.

After is, the adjective usually stays in its basic form:

• Die deur is wyd.
• Die kamer is groot.
• Die boek is interessant.

Before a noun, the adjective often takes -e:

• die wye deur
• die groot kamer
• die interessante boek

So wyd is correct here because it comes after is, not directly before deur.

It can also mean through in other sentences, which can confuse learners.

For example:

• Ek loop deur die park. = I walk through the park.

But in Die deur is wyd, it clearly means door, because:

• it comes after the article die
• it is the subject of the sentence
• the sentence is describing it as wide

So here deur is definitely the noun door.

A rough guide for an English speaker is:

• Die ≈ dee
• deur ≈ a rounded vowel not exactly found in English, something like duhr with rounded lips
• is ≈ iss
• wyd ≈ roughly vayt / vight, with the w sounding more like an English v

A few helpful pronunciation notes:

• Afrikaans w is usually pronounced like an English v
• y in Afrikaans is not pronounced like English y in yes
• eu in deur has no perfect English equivalent

So the whole sentence is approximately: dee duhr iss vayt

Yes. This is a very normal simple statement pattern:

subject + verb + adjective

So:

• Die deur = subject
• is = verb
• wyd = description

This is very similar to English, which makes sentences like this easy for beginners.

Yes, but it changes the meaning.

• Die deur is wyd. = The door is wide.
  You mean a specific door.

• 'n deur is wyd. = A door is wide.
  This sounds more general or less specific.

So the original sentence uses die because it is talking about the door, not just a door.

Yes. They are clearly related words, and that is helpful for learners.

• Afrikaans wyd
• English wide

They do not look identical, but they are close in both form and meaning. Afrikaans has many words that English speakers can recognize like this, even if the spelling is a little different.