Solicitantul verifică semnătura și dovada plății.

-ul is the Romanian definite article for a masculine singular noun. Instead of putting a separate word like the before the noun, Romanian usually attaches the article to the end.

• solicitant = applicant
• solicitantul = the applicant

This is a very common feature of Romanian.

That -a is also the definite article, but here it is for feminine singular nouns.

• semnătură = signature

• semnătura = the signature

• dovadă = proof
• dovada = the proof

So Romanian marks definiteness at the end of the noun, and the ending changes depending on gender and number.

Because plății is in the genitive form, meaning of the payment.

In dovada plății, the second noun depends on the first one:

• dovada = the proof
• plății = of the payment

So dovada plății means the proof of the payment or more naturally proof of payment.

Compare:

• plata = the payment
• dovada plății = the proof of the payment

This is a very common Romanian structure: noun + genitive noun.

Verifică is the 3rd person singular present tense form of the verb a verifica = to check / to verify.

So it can mean:

• he checks
• she checks
• it checks

In this sentence, because the subject is solicitantul, it means the applicant checks/verifies.

Because Romanian usually uses a postposed definite article: the article is attached to the end of the noun instead of being placed before it.

Examples:

• băiat = boy

• băiatul = the boy

• fată = girl
• fata = the girl

So in your sentence:

• solicitantul = the applicant
• semnătura = the signature
• dovada = the proof

This is one of the main differences from English.

Yes, but the meaning would change.

For example:

• Un solicitant verifică o semnătură și o dovadă a plății.

This would mean something more like an applicant checks a signature and proof of the payment.

Your original sentence uses definite forms, so it refers to specific things already known from context:

• the applicant
• the signature
• the proof of payment

This is the normal subject–verb–object order:

• Solicitantul = subject
• verifică = verb
• semnătura și dovada plății = objects

Romanian word order can be more flexible than English, but this order is the most neutral and standard one.

Yes, și usually means and.

In this sentence it joins two direct objects:

• semnătura
• dovada plății

So the applicant checks both items.

Also note the pronunciation: și is pronounced roughly like shee.

A rough pronunciation is:

so-li-chee-TAN-tul ve-ri-FI-cuh sem-nuh-TU-ra shi do-VA-da PLUH-tsee

A few useful notes:

• ț sounds like ts
• ș sounds like sh
• ă is a short neutral vowel, similar to the a in sofa
• â / î is a different central vowel that English does not really have

So:

• solicitantul → the t is followed by ț nowhere here, but stress is on -tant-
• verifică → stress on fi
• semnătura → stress on tu
• plății → stress on plă

Yes, it matters because gender affects the article and some case forms.

• solicitant = masculine
• semnătură = feminine
• dovadă = feminine
• plată = feminine

That is why you get:

• solicitantul with masculine definite -ul
• semnătura, dovada with feminine definite -a
• plății with the feminine singular genitive/dative form

Gender is an important part of Romanian grammar, especially for articles and adjective agreement.

They are very important, because they affect both pronunciation and sometimes meaning.

In this sentence you have:

• ă in verifică, semnătura, dovadă, plății
• ș in și
• ț in plății? No, not in this word, but Romanian uses it in many others

Without diacritics, the sentence might still be understandable to some native speakers in informal writing, but it is not correct standard Romanian.

For example:

• și = and
• writing si instead is nonstandard and can be confusing

So learners should get used to reading and writing the diacritics correctly.

It can be either, depending on context.

• a verifica often means to check
• in more formal or administrative contexts, it can also mean to verify

In a sentence like this, especially if it is about documents, both are possible in English:

• The applicant checks the signature and the proof of payment
• The applicant verifies the signature and the proof of payment

So this is a good example of a Romanian verb that overlaps with more than one common English verb.