Finalement, nous rentrons à la maison et je prépare une omelette.

Here, finalement means finally, in the end, or eventually, depending on context.

In this sentence, it most naturally means something like finally or in the end: after other events, we go home and I make an omelette.

A useful warning: French finalement often means in the end more than dramatic English finally!. So you should always check the context.

Rentrer means to return or to go back, often to go home.

So nous rentrons à la maison suggests:

• we’re going back home
• we return home

If you said nous allons à la maison, that would sound less natural in many cases, because aller just means to go, while rentrer specifically gives the idea of returning.

Both rentrons and prépare are in the present tense:

• nous rentrons = we return / we are returning / we go back
• je prépare = I prepare / I am preparing / I make

French uses the present tense in many situations where English might also use:

• the simple present
• the present progressive
• even a narrative present

So depending on context, the sentence could be understood as:

• Finally, we go home and I make an omelette
• Finally, we’re going home and I’m making an omelette

Because the two actions have different subjects:

• nous rentrons à la maison = we go home
• je prépare une omelette = I make an omelette

So the sentence means that we are going home, but then I am the one who prepares the omelette.

If the speaker wanted to say we prepare an omelette, it would be:

• et nous préparons une omelette

In French, when saying at home or homeward/home, the expression is usually à la maison.

So:

• rentrer à la maison = to go home / return home
• être à la maison = to be at home

French normally needs the preposition and article here, unlike English, which can simply say home.

Because maison is a feminine noun: la maison.

The preposition à combines with:

• le → au
• les → aux

But it does not combine with la.

So:

• à + la maison = à la maison
• not au maison

It can correspond to several English translations depending on context:

• go home
• come home
• return home

The core idea of rentrer is returning. English chooses go, come, or return depending on perspective.

So in many learning contexts, nous rentrons à la maison is best understood as:

• we’re going home or
• we return home

Because French usually uses an article with countable singular nouns.

Une omelette means:

• an omelette
• one omelette

You normally would not say just je prépare omelette in French. The noun needs a determiner, so une is required here.

Because omelette is a feminine noun in French.

So:

• une omelette
• not un omelette

This is just something you need to learn with the noun: omelette = feminine.

Yes, in this sentence et simply links the two actions, just like and:

• nous rentrons à la maison
• et
• je prépare une omelette

So the structure is very straightforward: Finally, we go home, and I make an omelette.

Sometimes yes, but not always with exactly the same feel.

• à la maison = at home / home
• chez nous = at our place / to our place / in our home

In many contexts, rentrer chez nous is possible and natural:

• Finalement, nous rentrons chez nous...

But à la maison is the very common, basic expression learners usually meet first.

In rentrons, there is no -ent ending. It is the nous form of rentrer, ending in -ons:

• je rentre
• tu rentres
• il/elle rentre
• nous rentrons

The ending -ons is pronounced.

Also, a useful point for learners: the silent -ent ending happens in many ils/elles forms, such as ils rentrent, where the final -ent is not pronounced.

So:

• nous rentrons = pronounced with the -ons
• ils rentrent = the final -ent is silent

It could do either, depending on context.

French present tense can describe:

• a current event
• a habitual action
• a narrative sequence

So this sentence could mean:

• Finally, we go home and I make an omelette as part of a story or
• In the end, we usually go home and I make an omelette if the wider context suggests a routine

The context around the sentence tells you which reading is intended.