Die helfte van die brilraam is swart.

Because die is the Afrikaans definite article, meaning the. It is used for all genders and for both singular and plural nouns.

So here it appears once before helfte and once before brilraam:

• die helfte = the half
• die brilraam = the frame

Afrikaans does not have different forms like the for masculine/feminine/neuter. It just uses die.

helfte is the noun meaning half.

In standard Afrikaans, die helfte van ... is a very common way to say half of ...:

• die helfte van die koek = half of the cake
• die helfte van die brilraam = half of the frame

The word half also exists in Afrikaans, but helfte is the clearer noun form in this kind of structure.

van is the normal word for of in this pattern.

So:

• die helfte van die brilraam = half of the frame

In other contexts, van can also mean from, but here it clearly means of.

Yes. Afrikaans very often writes compound nouns as one word.

So:

• bril = glasses / spectacles
• raam = frame
• brilraam = glasses frame / spectacle frame

This is very normal in Afrikaans. English often separates these kinds of words more than Afrikaans does.

In Afrikaans, bril is usually treated as a singular noun meaning glasses or a pair of glasses.

So even though English uses a plural-looking word, Afrikaans usually uses singular grammar:

• my bril = my glasses
• die brilraam = the glasses frame

So brilraam is singular, and that is completely normal.

This is the normal word order for a simple statement in Afrikaans:

• subject
• verb
• complement

So:

• Die helfte van die brilraam = subject
• is = verb
• swart = complement

That is the same basic pattern as English:

• Half of the frame is black

Because after is, Afrikaans uses the basic form of the adjective.

So you say:

• is swart
• is groot
• is mooi

In this sentence, swart is a predicate adjective, so it stays in its plain form.

Yes, in the present tense of to be, Afrikaans uses is for all persons:

• ek is = I am
• jy is = you are
• hy is = he is
• ons is = we are
• hulle is = they are

So unlike English am / is / are, Afrikaans just uses is.

A rough guide is:

• die ≈ dee
• helfte ≈ HELF-tuh
• brilraam ≈ bril-rahm, with a long aa
• swart ≈ svahrt or svaart

A useful extra point: Afrikaans w usually sounds more like English v than English w.