Χτες η πεθερά μου μαγείρεψε για όλους και ο πεθερός μου έφερε γλυκό.

Greek word order is flexible, and it is very common to put a time word first for emphasis or to set the scene.
So Χτες η πεθερά μου μαγείρεψε... is literally something like Yesterday my mother-in-law cooked...

This sounds natural in Greek.

These are the definite articles:

• η = the for feminine singular nouns
• ο = the for masculine singular nouns

So:

• η πεθερά = the mother-in-law
• ο πεθερός = the father-in-law

Greek uses the article more regularly than English does.

In Greek, possessive words like μου often come after the noun.

So:

• η πεθερά μου = my mother-in-law
• ο πεθερός μου = my father-in-law

Literally, it is closer to the mother-in-law of me, but in natural English we say my mother-in-law.

They usually mean:

• πεθερά = mother-in-law
• πεθερός = father-in-law

These are standard family words in Greek.

Μαγείρεψε is the aorist form of μαγειρεύω (to cook).
Here it means cooked as a completed action in the past.

So:

• μαγειρεύω = I cook / I am cooking
• μαγείρεψε = he/she cooked

In this sentence, it refers to η πεθερά μου, so it means my mother-in-law cooked.

Greek often leaves out subject pronouns because the verb ending already shows the person and number.

So:

• μαγείρεψε already tells us he/she cooked
• έφερε already tells us he/she brought

The nouns η πεθερά μου and ο πεθερός μου make the subject clear, so pronouns like she and he are unnecessary.

Για όλους means for everyone or for all of them.

• για = for
• όλους = all (of them/everyone) in the masculine plural accusative form

It is όλους because για takes the accusative case.
Also, masculine plural can be used for a mixed group of people or for people in general.

Here γλυκό means dessert or something sweet.
Without an article, it sounds indefinite, like:

• brought dessert
• brought a dessert
• brought something sweet

Greek often omits the article in cases like this, especially when speaking generally about food or an indefinite item.

No. Γλυκό can mean different but related things depending on context:

• sweet as an adjective
• a sweet / candy
• dessert

In this sentence, because of έφερε γλυκό, the natural meaning is brought dessert or brought something sweet.

Έφερε is the aorist form of φέρνω, which means to bring.

So:

• φέρνω = I bring / I am bringing
• έφερε = he/she brought

Here it refers to ο πεθερός μου, so it means my father-in-law brought.

Greek allows more flexibility in word order than English.
This sentence follows a very natural Greek pattern:

• Χτες = time first
• η πεθερά μου = subject
• μαγείρεψε = verb
• για όλους = extra information
• και = and
• ο πεθερός μου = new subject
• έφερε γλυκό = verb + object

English depends more heavily on fixed word order, while Greek can move parts around more easily without changing the core meaning.

Yes. Because Greek word order is flexible, you could rearrange parts of it and still keep basically the same meaning, for example:

• Η πεθερά μου μαγείρεψε χτες για όλους και ο πεθερός μου έφερε γλυκό.
• Χτες μαγείρεψε η πεθερά μου για όλους και ο πεθερός μου έφερε γλυκό.

The main meaning stays the same, but the emphasis may shift slightly depending on what comes first.