Biała kreda leży obok gąbki, a drugi kawałek kredy spadł na podłogę.

Because kreda is a feminine noun in Polish, and adjectives must agree with the noun in gender, number, and case.

• kreda = feminine singular
• so biały changes to biała

This is the nominative singular feminine form of the adjective biały.

So:

• biały stół = white table
• biała kreda = white chalk
• białe krzesło = white chair

In Biała kreda leży..., kreda is in the nominative singular because it is the subject of the verb leży.

The subject is the thing that is doing or being something in the sentence. Here, the chalk is the thing that is lying somewhere.

So:

• kreda = nominative singular
• biała also matches it in nominative singular feminine

Because after kawałek (piece), Polish normally uses the genitive.

So:

• kreda = nominative
• kredy = genitive

kawałek kredy literally works like a piece of chalk, where of chalk is expressed by the genitive in Polish.

This pattern is very common:

• kawałek chleba = a piece of bread
• szklanka wody = a glass of water
• butelka mleka = a bottle of milk

Obok requires the genitive case, so gąbka changes to gąbki.

• gąbka = nominative singular
• gąbki = genitive singular

So:

• obok gąbki = next to / beside the sponge

This is something you usually just have to learn together with the preposition:

• obok + genitive

Because spadł na podłogę expresses movement toward a place: it fell onto the floor.

With na, Polish often makes this distinction:

• na + accusative = movement onto/to
• na + locative = location on

So:

• spadł na podłogę = it fell onto the floor
• leży na podłodze = it is lying on the floor

In your sentence, the action is a change of position, so podłogę is in the accusative.

Because the grammatical subject of that part of the sentence is drugi kawałek kredy.

The head noun there is kawałek, and kawałek is masculine. In the Polish past tense, the verb agrees with the subject in gender and number.

So:

• kawałek = masculine singular
• therefore spadł = masculine singular past

Even though kreda is feminine, it is not the main noun of the subject here. The subject is piece, not chalk.

Here a links two parts of the sentence, but it is not exactly the same as simple and.

Very roughly:

• i = and, adding information straightforwardly
• a = and / while / whereas, often with a slight contrast or shift

In this sentence:

• Biała kreda leży obok gąbki, a drugi kawałek kredy spadł na podłogę.

There is a natural contrast between the two situations:

• one piece of chalk is lying beside the sponge
• another piece fell to the floor

So a sounds very natural here.

It can suggest either, depending on context.

In this sentence, drugi kawałek kredy most naturally means:

• the second piece of chalk, or
• the other piece of chalk

If the context is about two pieces of chalk, English might translate it more naturally as the other piece of chalk. But grammatically, drugi is the ordinary word for second.

Because Polish often uses a more specific verb where English might simply use is.

• leżeć = to lie
• stać = to stand
• wisieć = to hang

So Biała kreda leży obok gąbki means literally The white chalk is lying next to the sponge, which is the normal Polish way to describe where it is.

Using jest would be much less natural here if you want to describe physical position.

Yes, Polish word order is more flexible than English, but different orders change the focus or emphasis.

The given sentence is neutral and natural:

• Biała kreda leży obok gąbki, a drugi kawałek kredy spadł na podłogę.

You could also move things around for emphasis, for example:

• Obok gąbki leży biała kreda...
  = emphasis on where the chalk is

But for a learner, the original version is a very good standard word order to copy.

Leży is the 3rd person singular present tense form of leżeć (to lie).

So:

• ja leżę = I am lying
• ty leżysz = you are lying
• on / ona / ono leży = he / she / it is lying

In your sentence, kreda is singular, so leży is the correct form.

Yes, possibly, but the meaning is slightly different.

• obok gąbki = beside / next to the sponge
• przy gąbce = by / near the sponge

Obok usually sounds more specifically right next to, while przy can be a little looser. In your sentence, obok gąbki is a clear and natural choice.