Sy is tuis.

Here, Sy means she.

In Afrikaans, sy can be a subject pronoun, just like English she. Because it is the first word of the sentence, it is capitalized as Sy.

Afrikaans sy can also mean his, but the sentence structure tells you which meaning it has.

In Sy is tuis, sy is followed by the verb is, so Sy is the subject of the sentence: She is home.

If sy meant his, it would normally come before a noun, for example: sy huis = his house

So in this sentence, Sy must mean she.

Yes, very much so. is is the present-tense form of the verb to be, just like English is.

So: Sy is tuis = She is home

This is one of the nice things about this sentence: the structure is very close to English.

tuis means home or at home.

It describes being in one’s home place, not just any building. In English, we can say both She is home and She is at home; Afrikaans often uses tuis for that idea.

Because huis and tuis are not the same kind of word.

huis is a noun meaning house or sometimes home: Dit is my huis. = That is my house.

tuis means at home / home: Sy is tuis. = She is home.

So you use tuis when talking about someone’s location or state of being at home, not huis by itself.

Because tuis already includes the idea of at home.

English often needs a preposition: at home. Afrikaans can express that same idea with the single word tuis. So Sy is tuis is completely natural and complete.

Yes, you can, but it is not exactly the same in feel.

Sy is tuis means She is home in the natural, idiomatic sense.

Sy is by die huis is more like She is at the house / by the house. It focuses more on physical location and can sound less idiomatic if you simply mean she is home.

So if you want the most natural translation of She is home, Sy is tuis is the best choice.

A rough guide is:

Sy: roughly like say, but not exactly the same vowel
is: often a short unstressed is/uhs sound
tuis: the ui sound is tricky for English speakers and does not have a perfect English equivalent

The hardest part is usually tuis. It is best learned by listening to native pronunciation, because the Afrikaans ui sound is unfamiliar to most English speakers.

To make it negative, Afrikaans usually uses double nie:

Sy is nie tuis nie. = She is not home.

To turn it into a yes/no question, you normally invert the verb and subject:

Is sy tuis? = Is she home?

So the pattern is very useful: Sy is tuis.
Sy is nie tuis nie.
Is sy tuis?