Verificăm prețul total.

Verificăm is 1st person plural, present tense of a verifica.

So the ending -ăm here tells you the subject is we. Romanian verbs usually carry enough information that the subject pronoun does not have to be stated.

Romanian often drops subject pronouns because the verb ending already shows who is doing the action.

So Verificăm by itself already means we check / we are checking.
You could say Noi verificăm prețul total, but noi would usually add emphasis, like we in particular.

Because Romanian usually puts the definite article at the end of the noun instead of using a separate word like English the.

• preț = price
• prețul = the price

So prețul total is literally something like price-the total, but naturally it corresponds to the total price.

In Romanian, adjectives often come after the noun in the normal, neutral word order.

So:

• preț total = total price
• prețul total = the total price

Putting the adjective after the noun is very common and sounds natural here.

Because in this kind of phrase, Romanian normally marks definiteness on the noun, not on both words.

So prețul total is the standard pattern:

• prețul = the price
• total agrees as an adjective, but it does not get its own separate definite article here

This is normal Romanian structure.

It can mean either one, depending on context.

Romanian does not usually have a separate verb form like English we are checking for the continuous meaning. The simple present verificăm can cover both:

• we check
• we are checking

Context tells you which is meant.

Preț is a neuter noun.

In Romanian, neuter nouns behave:

• like masculine in the singular
• like feminine in the plural

That is why in the singular you get prețul, with the masculine/neuter singular definite article ending -ul.

Two important letters here are:

• ț in prețul: pronounced like ts in cats
• ă in verificăm: a short central vowel, similar to the weak vowel in the final sound of sofa

A rough pronunciation guide:

• verificăm ≈ veh-ree-fee-KUM
• prețul ≈ PREH-tsul
• total ≈ toh-TAL

The stress is usually:

• verificăm
• prețul
• total

Yes, that is grammatically correct.

But in normal Romanian, noi is often unnecessary because verificăm already shows we. Adding noi usually gives extra emphasis, for example if you want to contrast we with someone else.

So the shorter Verificăm prețul total is the most neutral version.