Learn Hardcore Swahili: Barua iliyo mezani ni ya mwalimu. - The letter that is on the table is the teacher's.

Both are correct. The -o form is shorter and very common in speech; the ambayo form is a bit heavier and can feel more formal or helpful in very long clauses.

Should it be iliyoko or iliyopo instead of iliyo?

All are possible, with nuance:

iliyo mezani: perfectly normal; often used without adding -ko/-po.
iliyoko mezani: explicitly “which is located on the table” (neutral/default location).
iliyopo mezani: also “which is located on the table,” with a sense of a specific/definite spot.
Use -mo (e.g., iliyomo) if something is inside a place.

You’ll hear all of these; adding -ko/-po/-mo just makes the locative sense explicit.

Does the -li- in iliyo mean past tense?

Not here. In these short relative forms of kuwa (to be) like aliye, iliyo, kilicho, the -li- is conventional and does not force a past meaning. If you really want to mark past, use:

ambayo ilikuwa mezani or iliyokuwa mezani = which was on the table.

What exactly does mezani mean, and how is it formed?

meza = table
mezani = at/on the table (meza + locative suffix -ni)

The locative -ni often covers at/in/on. For a more explicit “on top of,” use juu ya meza. You can also say kwenye meza for “on/at the table.”

Why is it ni ya mwalimu and not ni wa mwalimu?

Because the connective -a agrees with the possessed noun, not the possessor. The possessed item is barua (class 9), so you use the class 9 form ya:

barua ya mwalimu = the teacher’s letter Compare:
kitabu cha mwalimu (class 7: kitabu → cha)
viti vya mwalimu (class 8: viti → vya)

The possessor (mwalimu) does not determine the form of -a.

Is ni required here, and how do I negate the sentence?

Yes, ni is the copula meaning “is.” Without it, you’d just have a noun phrase, not a full sentence.

Negation:

Barua iliyo mezani si ya mwalimu.
You’ll also hear sio/siyo: … siyo ya mwalimu.

Past/future:

… ilikuwa ya mwalimu (was)
… itakuwa ya mwalimu (will be)

How would this change if I mean “letters” (plural)?

Use class 10 agreement for the relative and the connective:

Barua zilizo mezani ni za mwalimu. Notes:
barua is both singular and plural in form.
Relative: zilizo (class 10)
Connective: za (class 10)

Where does the relative clause go? Can I move it?

In neutral style, the relative clause follows the noun it describes:

Natural: Barua iliyo mezani ni ya mwalimu. Fronting it (e.g., Iliyo mezani barua…) is possible but marked/special. Keeping it right after barua is the safest and most natural.

Does ya mwalimu mean “for the teacher”?

No. ya mwalimu means “of/belonging to the teacher.” For “for the teacher,” use:

kwa mwalimu or kwa ajili ya mwalimu (for the teacher/for the benefit of the teacher).

Can I replace ya mwalimu with a possessive pronoun?

Yes. Use a possessive that agrees with barua (class 9):

Barua iliyo mezani ni yake. = The letter … is his/hers. Other examples with class-9 agreement: yangu (mine), yetu (ours), yenu (yours pl.).

Can I say Barua ya mwalimu iliyo mezani? Is that different?

Yes. Both are grammatical but differ in focus:

Barua iliyo mezani ni ya mwalimu. Focuses first on “the letter on the table,” then states it belongs to the teacher.
Barua ya mwalimu iliyo mezani … Starts by identifying it as “the teacher’s letter,” then specifies which one (the one on the table).

Could I use yenye here (e.g., barua yenye…)?

No. -enye means “having/with.” Use it for inherent features, e.g., barua yenye stempu (a letter with a stamp). For location, use the relative forms: iliyo/iliyoko/iliyopo or ambayo iko.

Why is there no word for “the” in barua?

Swahili doesn’t have articles like “a/the.” Definiteness comes from context and modifiers. The relative clause iliyo mezani effectively makes barua specific, like English “the letter that is on the table.”