Kuppi on pöydällä, ja minä kaadan siihen teetä.

Because Finnish uses cases where English often uses prepositions.

Pöydällä is the adessive case of pöytä (table), and here it means on the table.

• pöytä = table
• pöydällä = on the table / at the table

So Kuppi on pöydällä literally looks like Cup is table-on, but in natural English it means The cup is on the table.

Because siihen means into it / into that, while siinä means in it / in that.

This is an important Finnish distinction:

• siinä = in it, inside it, there in it
• siihen = into it, into that

In this sentence, tea is being poured into the cup, so Finnish uses the form that shows movement toward the inside:

• kaadan siihen teetä = I pour tea into it

If you said siinä, it would suggest location rather than movement.

It refers back to kuppi (the cup).

So:

• Kuppi on pöydällä = The cup is on the table
• kaadan siihen teetä = I pour tea into it

Finnish often avoids repeating the noun if it is already clear from context, just like English can say into it instead of into the cup.

Because teetä is the partitive form of tee.

Here the partitive is used because the sentence is talking about some tea, not a whole clearly completed amount. With liquids and other uncountable substances, Finnish very often uses the partitive when you mean some of something.

• tee = tea
• teetä = some tea / tea as an uncountable substance

So kaadan siihen teetä means I pour some tea into it or I am pouring tea into it.

Yes, but the meaning would change.

• kaadan siihen teetä = I pour some tea into it / I am pouring tea into it
• kaadan siihen teen = I pour the tea into it / I pour all of the tea into it

Very roughly:

• partitive (teetä) = an ongoing, indefinite, or partial amount
• total object (teen) = a complete, definite amount

In this sentence, teetä is the more natural choice if the idea is simply that tea is being poured into the cup.

Yes, kaadan already shows that the subject is I, because the verb ending tells you the person.

• kaadan = I pour

So minä is not strictly necessary. Finnish often drops subject pronouns when the verb already makes the subject clear.

However, minä can still be included for:

• emphasis
• clarity
• contrast
• a slightly more explicit style

So both are possible:

• ja kaadan siihen teetä
• ja minä kaadan siihen teetä

The version with minä sounds a bit more explicit: and I pour tea into it.

Kaadan is the 1st person singular present tense form of the verb kaataa.

• kaataa = to pour
• kaadan = I pour

Some other forms are:

• kaadat = you pour
• kaataa = he/she/it pours
• kaadamme = we pour
• kaadatte = you all pour
• kaatavat = they pour

So in this sentence, minä kaadan simply means I pour.

Both are possible, but the emphasis is a little different.

• Kuppi on pöydällä = The cup is on the table.
• Pöydällä on kuppi = There is a cup on the table.

The version in your sentence starts with kuppi, so it feels like the cup is already the topic. Then the next clause naturally continues by referring to it with siihen.

So this structure is very logical:

1. mention the cup
2. say where it is
3. say that you pour tea into it

Finnish normally does not have articles like a or the.

So:

• kuppi can mean a cup or the cup
• pöytä can mean a table or the table

Context tells you which meaning is intended.

In Kuppi on pöydällä, English usually translates it as The cup is on the table, because the sentence sounds like it is talking about a specific cup and a specific table already understood from context.

They show two different kinds of spatial meaning.

• pöydällä = on the table
  This is surface location, using the adessive case.
• siihen = into it
  This is movement into something, using the illative form.

So Finnish does not use one general preposition like English sometimes does. Instead, it chooses a case based on the kind of relationship:

• being on a surface → -lla / -llä
• moving into something → special illative form like siihen

That is why the sentence uses two different forms.

Yes, absolutely.

• kaadan siihen teetä = I pour tea into it
• kaadan kuppiin teetä = I pour tea into the cup

Both are correct. The difference is that siihen refers back to the cup, while kuppiin repeats the noun directly.

Using siihen sounds natural because kuppi was just mentioned in the previous clause.

Ja simply means and.

It connects the two clauses:

• Kuppi on pöydällä = The cup is on the table
• ja minä kaadan siihen teetä = and I pour tea into it

So the whole sentence is made of two linked statements.

In Finnish, the present tense can do both jobs.

So minä kaadan siihen teetä can mean:

• I pour tea into it
• I am pouring tea into it

Finnish does not usually have a separate verb form like English am pouring. The context tells you whether the meaning is habitual or happening now.

In this sentence, most learners would naturally understand it as something happening in the situation being described: The cup is on the table, and I am pouring tea into it.