Adoptăm animalul de companie de la adăpostul de animale.

Yes. Adoptăm is the 1st person plural present tense of a adopta = to adopt.

So it can mean:

• we adopt
• we are adopting

Romanian does not usually make the same simple-vs-progressive distinction that English does. The present tense often covers both, and context tells you which meaning is intended.

Also, adoptăm by itself is normally not let’s adopt. For that, Romanian usually uses să adoptăm.

Because Romanian verbs usually already show the subject clearly.

In adoptăm, the ending -ăm tells you the subject is we. So noi is not necessary.

• Adoptăm animalul... = We adopt / We are adopting the pet...
• Noi adoptăm animalul... = same basic meaning, but with extra emphasis on we

Romanian often leaves subject pronouns out unless there is contrast or emphasis.

Romanian usually puts the definite article at the end of the noun, not in front of it.

So:

• animal = animal
• animalul = the animal

and:

• adăpost = shelter
• adăpostul = the shelter

This is one of the most important differences from English. Instead of a separate word like the, Romanian often adds an ending to the noun.

It means the pet.

Literally, it is something like the animal for companionship or the companion animal, but the normal meaning is simply the pet.

You will also see:

• animal de companie = a pet
• animalul de companie = the pet
• animale de companie = pets

So de companie works as a set expression meaning pet / kept as a companion.

Here de links the noun to a category or description.

So animal de companie is not really about possession. It is a fixed descriptive structure meaning something like:

• an animal for companionship
• a companion animal
• a pet

Romanian uses de very often in noun combinations like this. A few similar patterns are:

• periuță de dinți = toothbrush
• sală de sport = gym
• adăpost de animale = animal shelter

So in this sentence, de helps build the expression animal de companie.

De la means from, especially when talking about a source, person, institution, or place you get something from.

So:

• de la adăpostul de animale = from the animal shelter

In this sentence, the shelter is the source from which the pet is adopted.

This is a very common Romanian pattern:

• luăm ceva de la magazin = we get something from the store
• cumpărăm de la fermă = we buy from the farm

This is a very good question, because both can sometimes translate as from.

• de la usually means from a source / from someone / from an institution or place
• din usually means out of / from inside

So:

• adoptăm animalul de companie de la adăpost = we adopt the pet from the shelter
• scoatem animalul din adăpost = we take the animal out of the shelter

In an adoption context, de la is the natural choice because the shelter is the source or provider.

Both are possible Romanian structures, but they are not used in exactly the same way.

• adăpost de animale = animal shelter as a type/category
• adăpostul de animale = the animal shelter

This is the normal, idiomatic way to say animal shelter.

By contrast:

• adăpostul animalelor means more literally the shelter of the animals or the animals’ shelter

That version sounds more specific or more literal, not like the standard name of the institution.

So in this sentence, adăpostul de animale is the natural choice.

Because in Romanian, when a noun is part of a category expression after de, it often stays indefinite.

So:

• adăpost de animale = animal shelter
• adăpostul de animale = the animal shelter

The main noun, adăpostul, carries the definiteness. The second noun, animale, just tells you what kind of shelter it is.

This is very common in Romanian:

• magazin de haine = clothing store
• stație de autobuz = bus stop
• sală de sport = gym

So animale here does not need a separate definite form.

The given order is the most neutral one:

• Adoptăm animalul de companie de la adăpostul de animale.

This is a normal verb + object + prepositional phrase order.

Romanian word order is fairly flexible, though. You can move things for emphasis, but the sentence may sound more marked or may need a clitic pronoun. For example:

• Animalul de companie îl adoptăm de la adăpostul de animale.

This puts extra emphasis on animalul de companie.

So the original version is the best neutral choice for a basic statement.