Na talerzu została tylko mała kromka chleba, więc zrobię kanapkę dopiero po pracy.

Because Polish uses na for something being on the surface of a plate, table, shelf, etc.

• na talerzu = on the plate
• w talerzu would sound unnatural in this context, because food is normally thought of as lying on a plate, not inside it.

Also, na talerzu uses the locative case after na when it means location.

Here została means remained or was left.

So:

• Na talerzu została tylko mała kromka chleba
  = Only a small slice of bread was left on the plate

The ending -ła shows that the subject is feminine singular. The subject here is kromka (slice), and kromka is a feminine noun.

Compare:

• został = masculine singular
• została = feminine singular
• zostało = neuter singular
• zostały = non-masculine personal plural

Polish past tense verbs agree with the subject in gender and number.

Tylko means only, and in this sentence it emphasizes what remained:

• została tylko mała kromka chleba
  = only a small slice of bread remained

Its position is quite natural here. It tells you that what was left was just that, and nothing more.

Polish word order is flexible, but this placement sounds very normal and clear.

Kromka means a slice, especially a slice of bread cut from a loaf.

So:

• kromka chleba = a slice of bread

This is more specific than a general piece:

• kromka chleba = slice of bread
• kawałek chleba = piece of bread

A learner should know that kromka is a very common word when talking about bread.

Because after a noun like kromka (slice), Polish usually puts the second noun in the genitive case.

So:

• kromka chleba = a slice of bread
• szklanka wody = a glass of water
• butelka mleka = a bottle of milk

The basic noun is chleb, but in the genitive singular it becomes chleba.

This is a very common Polish pattern: container / measure / part + genitive.

Więc means so, therefore, or as a result.

It connects the two parts of the sentence:

• Only a small slice of bread was left on the plate, so I’ll make a sandwich only after work.

It is a very common linking word in everyday Polish.

A close equivalent is więc = so in ordinary spoken English.

Because zrobię is the future tense of a perfective verb: zrobić.

In Polish:

• robić = imperfective, to do / to make in an ongoing or repeated sense
• zrobić = perfective, to do / to make as a completed action

So:

• zrobię kanapkę = I’ll make a sandwich / I’ll prepare a sandwich
  with the idea of a single completed action

If you said będę robić kanapkę, it would sound more like:

• I’ll be making a sandwich
• or it might emphasize the process rather than the finished result

Here, zrobię is the natural choice.

Because kanapkę is the accusative singular, and it is the direct object of zrobię.

• kanapka = nominative
• zrobię kanapkę = I will make a sandwich

For many feminine nouns ending in -a, the singular accusative ends in -ę:

• kawa → piję kawę
• książka → czytam książkę
• kanapka → zrobię kanapkę

So this is a very useful pattern to remember.

Yes, absolutely. It is very natural.

Polish often uses zrobić with food in the sense of make / prepare:

• zrobić kanapkę = make a sandwich
• zrobić obiad = make lunch / prepare dinner
• zrobić kawę = make coffee

So even though the literal verb is do/make, the phrase sounds completely normal.

Here dopiero means not until or only then.

So:

• dopiero po pracy = not until after work

This word often adds the idea of later than expected or only at that point.

Examples:

• Przyjdę dopiero wieczorem = I’ll come only in the evening / not until the evening
• Zrobię kanapkę dopiero po pracy = I’ll make a sandwich only after work / not until after work

So dopiero is very important for the nuance of timing.

After po meaning after, Polish uses the locative case.

So:

• po pracy = after work

The noun praca becomes pracy in the locative singular.

This is worth noticing because pracy also looks like the genitive form, but here its function is locative, because it follows po in the sense of after.

Other examples:

• po obiedzie = after dinner
• po lekcji = after class
• po spotkaniu = after the meeting

Yes, the word order is natural.

Polish has fairly flexible word order, and the sentence begins with Na talerzu to set the scene:

• Na talerzu została tylko mała kromka chleba...

This sounds natural because it first tells you where the remaining bread is.

You could rearrange parts of the sentence, but the emphasis would change. For example:

• Tylko mała kromka chleba została na talerzu...
• Została na talerzu tylko mała kromka chleba...

These are possible, but the original version is smooth and idiomatic.

So the word order is not random: it helps organize what is already known or important in context.