Mia avo venas dimanĉe, kaj mia avino preparas teon por ni.

Because avino is built from avo with the suffix -in-, which marks a female person.

• avo = grandfather
• avino = grandmother

This is a very common Esperanto pattern:

• patro = father, patrino = mother
• frato = brother, fratino = sister

So learning -in- is very useful.

Mia means my.

It is a possessive word, like an adjective, and here it stays mia both times because both nouns are:

• singular
• not in the accusative

If the noun changed, mia could change too:

• miaj geavoj = my grandparents
• mian avon = my grandfather (as a direct object)

So in this sentence, mia avo and mia avino are both singular subjects, so mia is the correct form.

In Esperanto, a possessive like mia, via, lia, etc. usually makes la unnecessary.

So you normally say:

• mia avo = my grandfather

not:

• la mia avo

This works much like English, where we say my grandfather, not the my grandfather.

Because -as is the present-tense verb ending in Esperanto.

• venas = comes / is coming
• preparas = prepares / is preparing

Esperanto verbs do not change form for different persons:

• mi venas = I come
• vi venas = you come
• li venas = he comes
• ili venas = they come

So the ending tells you the tense, not the person.

Esperanto often uses the present tense for a planned or expected future event when the time is already clear from context.

So:

• Mia avo venas dimanĉe
  can mean
• My grandfather is coming on Sunday

This is similar to English, where we often use is coming for the future.

You could also say:

• Mia avo venos dimanĉe

That would make the future more explicit. Both are possible, but venas dimanĉe is very natural.

Dimanĉo is the noun Sunday.

The form dimanĉe is an adverb meaning:

• on Sunday
• sometimes on Sundays, depending on context

The ending -e makes it adverbial, so it expresses time.

Compare:

• dimanĉo = Sunday
• dimanĉe = on Sunday

This is a very common way to talk about days in Esperanto.

It can mean either, depending on context.

In a sentence like this one, most people would understand it as a specific Sunday:

• My grandfather is coming on Sunday

But in another context, dimanĉe could also mean on Sundays in general.

If you need to be more specific, you can add extra words, for example:

• ĉi-dimanĉe = this Sunday
• ĉiun dimanĉon = every Sunday

Because teon is the direct object of preparas.

In Esperanto, the direct object usually takes -n.

• teo = tea
• teon = tea (as the thing being prepared)

So:

• mia avino preparas teon = my grandmother prepares tea

The -n tells you what is being prepared.

Because por is a preposition, and after a preposition Esperanto normally uses the basic form of the noun or pronoun.

So:

• por ni = for us

not:

• por nin

Compare:

• Ŝi vidas nin = She sees us.
  Here nin is a direct object, so it gets -n.

• Ŝi preparas teon por ni = She prepares tea for us.
  Here ni comes after por, so no -n.

Kaj means and.

It joins the two parts of the sentence:

• Mia avo venas dimanĉe
• mia avino preparas teon por ni

So the whole sentence gives two related pieces of information.

Yes, Esperanto word order is fairly flexible because endings show the grammatical roles clearly.

The normal, easiest order is:

• Mia avino preparas teon por ni

But you could also say things like:

• Por ni mia avino preparas teon

That changes the emphasis a bit, but the meaning stays basically the same.

For learners, though, the standard subject-verb-object order is usually best.

The comma separates two full clauses:

• Mia avo venas dimanĉe
• mia avino preparas teon por ni

In Esperanto, punctuation is somewhat flexible, and some writers would omit the comma before kaj. But using it here is completely acceptable, especially because each side has its own subject and verb.