Στον έλεγχο της Παρασκευής έκανα λιγότερα λάθη από ό,τι στο προηγούμενο μάθημα.

Yes. Στον is the usual contracted form of σε + τον.

A few very common contractions are:

• σε + τον → στον
• σε + τη(ν) → στην
• σε + το → στο

So Στον έλεγχο is simply σε τον έλεγχο in a more natural, standard form.

It can mean check, inspection, or control in other contexts, but in a school context έλεγχος can also mean a test or quiz.

So στον έλεγχο here means something like:

• in the test
• on the test

Greek σε is broader than English in/on/at, so the exact English preposition depends on how you choose to translate it.

Because της Παρασκευής is genitive, and here it means of Friday or Friday’s.

So:

• ο έλεγχος της Παρασκευής = Friday’s test / the Friday test

By contrast:

• την Παρασκευή means on Friday

So the sentence is talking about the test of Friday, not simply saying that something happened on Friday.

Έκανα is the past form of κάνω, which means do or make.

In this sentence, it means I made:

• έκανα λάθη = I made mistakes

With κάνω, the form έκανα can sometimes depend on context for its exact aspect, but here the meaning is clearly a simple past event: the speaker is talking about the result of one specific test.

Because λιγότερα has to agree with λάθη.

• λάθος = mistake
• λάθη = mistakes

Λάθη is neuter plural, so the comparative adjective must also be neuter plural:

• λιγότερα λάθη = fewer mistakes

Compare the forms of λιγότερος:

• masculine: λιγότερος
• feminine: λιγότερη
• neuter: λιγότερο

Plural neuter:

• λιγότερα

So λιγότερα λάθη is the correct agreement.

Yes. Both are possible.

• λιγότερα λάθη
• πιο λίγα λάθη

Both mean fewer mistakes. In this sentence, λιγότερα is a very natural and standard choice.

For learners, it is useful to recognize that Greek comparatives can often be formed in two ways:

• with a comparative form like λιγότερα
• with πιο
  • the basic adjective, like πιο λίγα

It introduces the comparison: than.

So:

• λιγότερα λάθη από ό,τι... = fewer mistakes than...

What follows is really an understood clause, not just a simple noun phrase. The full idea is:

• έκανα λιγότερα λάθη από ό,τι έκανα στο προηγούμενο μάθημα

The second έκανα is omitted because it is already clear.

So the sentence is basically:

• I made fewer mistakes than I did in the previous lesson

Because these are two different words in standard spelling:

• ότι = that
• ό,τι = whatever / what

In από ό,τι, Greek uses ό,τι, not ότι.

So this is not the that word. It is the form used in this comparative structure.

This is a very common spelling point for learners, because the pronunciation is the same, but the spelling and meaning are different.

For the same reason as στον earlier:

• στο = σε + το

Also, μάθημα is a neuter noun, so the article is το.

The adjective προηγούμενο agrees with μάθημα:

• το προηγούμενο μάθημα = the previous lesson / class

After σε, Greek uses the accusative, and for neuter nouns like μάθημα, the accusative form is the same as the nominative:

• το μάθημα
• στο μάθημα

Yes, it could.

Greek word order is more flexible than English word order. The sentence begins with Στον έλεγχο της Παρασκευής to set the scene first:

• As for the Friday test...
• In the Friday test...

A more neutral order could be:

• Έκανα λιγότερα λάθη στον έλεγχο της Παρασκευής από ό,τι στο προηγούμενο μάθημα.

Both are correct. The original version gives a little more emphasis to the Friday test as the context.