Learn Hardcore Swahili: Riwaya ninayoisoma sasa inasimulia kisa cha msichana anayejifunza lugha tatu kwa wakati mmoja. - The novel I am reading now tells the story of a girl who is learning three languages at the same time.

ni- = I (1st person singular subject prefix)
-na- = present tense marker (am / is / are doing)
-yo- = relative marker agreeing with riwaya (noun class 9), meaning which / that
-i- = object marker for class 9 (it, referring back to riwaya)
som = verb root read
-a = final vowel (marks the normal verb form)

So ninayoisoma literally corresponds to I-am-which-it-read, i.e. (that) I am reading (it).
In context, riwaya ninayoisoma sasa = the novel (that) I am reading now.

Why do we need both -yo- and -i- in ninayoisoma? Could I just say ninayosoma?

The two pieces do different jobs:

-yo- is the relative marker agreeing with riwaya. It turns the clause into a relative clause (which / that).
-i- is the object marker for a class‑9 noun (it, referring to riwaya).

So ninayoisoma is literally I-am-[REL]-it-read, (that) I am reading it.

In everyday spoken Swahili many people actually would say riwaya ninayosoma sasa (dropping -i-) and it is widely understood.
In more careful or traditional grammar, ninayoisoma (with both -yo- and -i-) is the fully marked form.

Why is there no separate word for which / that before ninayoisoma?

In Swahili, relative meaning (who, which, that) is usually built into the verb with a special marker, instead of using a separate word like English that:

riwaya ninayoisoma = the novel that I am reading
(-yo- inside ninayoisoma is doing the job of that/which)

So you do not say something like riwaya ambayo ninayoisoma unless you want a longer, more explicit style.
Both are possible, but the verb-with-relative-marker pattern (ninayoisoma, anayejifunza, ninalokipenda, etc.) is extremely common and very natural.

How does anayejifunza mean who is learning? What are its parts?

anayejifunza is also a relative verb form. Breakdown:

a- = he/she (subject marker for noun class 1, matching msichana)
-na- = present tense (is doing)
-ye- = relative marker for class 1 (who / that)
-ji- = reflexive marker (oneself)
funz = root from fundisha / funza (teach)
-a = final vowel

Literally: he/she-is-who-self-teach, i.e. who is learning (teaching herself).

So:

msichana anayejifunza lugha tatu
= a girl who is learning three languages

You could also say msichana ambaye anajifunza lugha tatu (with the separate relative word ambaye), but anayejifunza is shorter and very natural.

What does jifunza literally mean? Why not just a verb that means to learn?

The basic idea is:

fundisha / funza = to teach (someone)
jifunza = to teach oneself, i.e. to learn

So kujifunza is literally to teach oneself, which Swahili uses for to learn.
In many contexts when you see -jifunza attached to a subject (e.g. anajifunza, wanajifunza), you can safely translate it as is learning / are learning.

Why does riwaya go with inasimulia and not something like yinasimulia or anasimulia?

Swahili verbs agree with the noun class of the subject, not with gender as in many European languages.

riwaya belongs to noun class 9 (same form in singular and plural).
The subject prefix for class 9 is i-.
With present tense -na- and root simuli we get:
i- + -na- + simuli + -a → inasimulia

So:

riwaya inasimulia... = the novel tells / narrates...

If the subject were msichana (class 1), the verb would start with a-:

msichana anasimulia... = the girl tells...

In kisa cha msichana, why is it cha and not wa or la? What does cha agree with?

In possessive X of Y constructions, the possessive connector agrees with the thing possessed, not with the owner.

Here:

kisa = story / incident, class 7 (ki-/vi-)
The possessive connector for class 7 is cha
msichana = girl, class 1 (but it does not control the form of cha here)

So:

kisa cha msichana = the story of a girl
literally: story (class 7) + of‑class‑7 + girl

Some comparisons:

kisa cha msichana – story of a girl (class 7 → cha)
gari la msichana – the girl’s car (class 5 gari → la)
nyumba ya msichana – the girl’s house (class 9 nyumba → ya)
kitabu cha mwalimu – the teacher’s book (class 7 kitabu → cha again)

So cha is there because kisa is class 7.

Since lugha can be both language and languages, how do I know whether lugha here is singular or plural?

You rely on context and agreement, because for many class 9/10 nouns the singular and plural form of the noun itself is identical.

lugha = language / languages (class 9/10)

In this sentence you see:

lugha tatu = three languages

The numeral tatu (three) tells you clearly there are several languages, so lugha must be understood as plural here.

In other sentences you might see agreement on verbs or adjectives to show plural, e.g.:

lugha hizi ni ngumu = these languages are difficult
(hizi and ni are plural here)

Why is it lugha tatu and not lugha watatu, like wasichana watatu?

Number agreement in Swahili works differently for human vs non‑human nouns and also depends on the specific number.

For people/animals in class 1/2, you commonly see wa- with numbers from 3 upwards:
- msichana mmoja – one girl
- wasichana wawili – two girls
- wasichana watatu – three girls
- wasichana wanne – four girls
For many non‑human nouns (like lugha, class 9/10), from tatu upwards the number often appears without a class prefix:
- lugha tatu – three languages
- vitabu vitatu or more simply vitabu tatu – three books
- meza tatu – three tables

So lugha tatu is correct because lugha is not a human noun; watatu is reserved for people/animals in class 1/2 (and some similar cases), e.g. wasichana watatu, watoto watatu.

What does kwa wakati mmoja add? Could I just say wakati mmoja?

wakati mmoja on its own is one time / one occasion / one moment.
kwa wakati mmoja is used adverbially and is best translated as at the same time / simultaneously.

The preposition kwa is very flexible; here it turns wakati mmoja into an adverbial phrase:

anayejifunza lugha tatu kwa wakati mmoja
= who is learning three languages at the same time

You could sometimes say just wakati mmoja and be understood from context, but kwa wakati mmoja is the standard, natural way to express simultaneously / at once in this kind of sentence.

Why do we say msichana anayejifunza lugha tatu kwa wakati mmoja instead of just msichana anajifunza lugha tatu kwa wakati mmoja?

Both structures are grammatically correct, but they work differently:

msichana anayejifunza lugha tatu kwa wakati mmoja
= a girl who is learning three languages at the same time
→ anayejifunza is a relative form, describing which girl.
msichana anajifunza lugha tatu kwa wakati mmoja
= the girl is learning three languages at the same time
→ this is a full main clause, talking about the girl as the subject of a sentence.

In the original sentence, msichana anayejifunza... is part of a larger noun phrase kisa cha msichana anayejifunza..., which all together is the story being told by the novel.
So we need the relative form (anayejifunza) to tightly describe that particular girl inside the noun phrase.