După curs ne este foame și mergem la un restaurant mic de lângă piață.

Because foame works like a noun in Romanian, not like an adjective meaning hungry.

So Romanian expresses this idea more like:

to us is hunger

• ne = to us
• este = is
• foame = hunger

That is why este stays singular: it agrees with foame, not with we.

A more adjective-like alternative also exists:

• suntem flămânzi = we are hungry

But ne este foame is extremely common and natural.

Ne is the unstressed pronoun meaning to us in this sentence.

In ne este foame, it marks the person experiencing the feeling:

• mi-e foame = I am hungry
• ți-e foame = you are hungry
• îi este foame = he/she is hungry
• ne este foame = we are hungry
• vă este foame = you (plural/formal) are hungry
• le este foame = they are hungry

So ne is not the subject we. It is more like an indirect object: to us.

Because grammatically the core idea is foame este, not noi suntem.

Romanian is treating foame as the thing that is, and ne as the experiencer:

• literally: to us is hunger

So the verb is singular:

• ne este foame

This same pattern appears with other feelings or states:

• mi-e sete = I am thirsty
• îi este frig = he/she is cold
• ne este somn = we are sleepy

Because Romanian usually drops subject pronouns when they are not needed.

The ending of the verb already tells you who the subject is:

• merg = I go
• mergi = you go
• merge = he/she goes
• mergem = we go
• mergeți = you (plural) go
• merg = they go

So mergem already means we go. You could say noi mergem, but that usually adds emphasis or contrast.

Mergem is the 1st person plural, present tense of a merge = to go.

So:

• eu merg = I go
• noi mergem = we go

In this sentence, mergem la un restaurant... means we go to a restaurant...

Because a merge la is the normal way to say to go to a place.

• mergem la un restaurant = we go to a restaurant

If you said într-un restaurant, that would focus more on being inside a restaurant, not on the destination itself.

So:

• mergem la restaurant = we’re going to the restaurant
• suntem într-un restaurant = we are in a restaurant

In Romanian, adjectives usually come after the noun.

So:

• un restaurant mic = a small restaurant
• o casă mare = a big house
• un oraș frumos = a beautiful city

Sometimes an adjective can come before the noun, but that is less neutral and can sound more expressive or literary. The normal order here is restaurant mic.

Yes, de lângă is a fixed expression meaning near, beside, or next to.

So:

• de lângă piață = near the market / next to the market square

You can think of it as a prepositional phrase:

• lângă = near / next to
• de lângă often means the one from/by/near

In this sentence, it describes which restaurant:

• un restaurant mic de lângă piață
• a small restaurant near the market

Piață without the article means a market / market square in a general sense.

So de lângă piață means near the market in a broad, non-specific way.

If you say piața, that means the market with the definite article attached:

• piață = market
• piața = the market

Both can be possible depending on context, but de lângă piață is very natural when the place is being identified in a general way.

Yes. După curs very naturally means after class or after the lesson.

Romanian often uses the singular in cases where English also uses a singular collective idea:

• după curs = after class
• după lecție = after the lesson

If you wanted to say after classes or after the courses in a more explicitly plural sense, you could use:

• după cursuri

But după curs is perfectly normal for after class.

Romanian often omits the article in time expressions or in expressions that are understood generically.

So după curs is a natural phrase meaning after class.

Compare:

• după școală = after school
• după masă = after lunch / in the afternoon (in some contexts)
• după curs = after class

You could sometimes see a definite form in other contexts, but here the bare noun sounds natural and idiomatic.

Here și simply means and:

• ne este foame și mergem...
• we are hungry and we go...

In other contexts, și can also mean also / too depending on placement and emphasis, but in this sentence it is the ordinary coordinating and.

Yes, Romanian word order is fairly flexible, but the given version is neutral and natural.

The sentence:

• După curs ne este foame și mergem la un restaurant mic de lângă piață.

sounds like standard everyday Romanian.

You could move some parts for emphasis, for example:

• După curs, mergem la un restaurant mic de lângă piață, fiindcă ne este foame.
• Ne este foame după curs și mergem la un restaurant mic de lângă piață.

But the original is a very good, normal order for learners to model.

The main special letters here are:

• ă in după, lângă, piață
• ț in piață
• ș in și

Roughly:

• ă = a short central vowel, like the a in English sofa
• ț = ts, like in cats
• ș = sh, like in ship

So approximately:

• după ≈ DOO-puh
• lângă ≈ LUHN-guh
• piață ≈ PYA-tsuh
• și ≈ shī

These are only approximations, but they help at the start.