El problema parece grave.

Because problema is one of the common Spanish nouns that end in -a but are still masculine.

So you say:

• el problema
• un problema
• los problemas

This happens with several words of Greek origin, such as:

• el sistema
• el tema
• el programa

So the -a ending does not always mean a noun is feminine.

Parece means seems or appears.

So:

• El problema es grave = The problem is serious.
• El problema parece grave = The problem seems serious.

Using parece makes the statement less definite. It suggests an impression or judgement rather than a firm fact.

You can sometimes say parece ser, but it is less direct and often unnecessary here:

• El problema parece grave = the most natural version
• El problema parece ser grave = possible, but more formal or wordy

Because the subject is el problema, which is third person singular.

The verb parecer is conjugated like this in the present:

• yo parezco
• tú pareces
• él / ella / usted parece
• nosotros parecemos
• vosotros parecéis
• ellos / ellas / ustedes parecen

Since el problema = it, you use parece.

In Spanish, after parecer, you can put an adjective directly.

So:

• parece grave = seems serious
• parece interesante = seems interesting
• parece difícil = seems difficult

This works very much like English, where you also say seems serious, not seems to be serious in the simplest version.

Here, grave means serious, severe, or grave in the formal English sense.

So in this sentence it means the problem is serious in importance or severity.

Be careful: English grave often makes people think first of the noun grave (a place where someone is buried), but that is not the meaning here.

In Spanish, grave commonly means:

• serious
• severe
• critical

Examples:

• una enfermedad grave = a serious illness
• un error grave = a serious mistake

Usually, the normal order is:

• el problema grave = the serious problem
• un problema grave = a serious problem

In Spanish, adjectives often come after the noun.

Putting grave before the noun is possible in some literary or emphatic styles, but it is not the default choice for learners. So for normal usage, stick with:

• un problema grave
• el problema parece grave

Normally, no—not for this kind of sentence.

For an abstract thing like problema, Spanish usually uses:

• es grave = is serious
• parece grave = seems serious

Está grave is much more common with people, health, or conditions that are in a critical state, for example:

• El paciente está grave = The patient is in a serious condition.

So with problema, parece grave is natural, while está grave would usually sound wrong or unnatural.

A simple guide is:

• parece ≈ pah-REH-theh in much of Spain
• grave ≈ GRAH-beh

A few useful pronunciation notes:

• In most of Spain, c before e is pronounced like th in think, so parece sounds like pa-RE-the.
• In Latin America and some parts of Spain, it sounds like s instead.
• The v in grave is pronounced very similarly to b in Spanish, not like the English v.
• The stress is on:
  • pa-RE-ce
  • GRA-ve

Because it is describing a masculine singular noun: el problema.

So the adjective stays grave.

Also, grave is an adjective whose singular form is the same for masculine and feminine:

• el problema grave
• la situación grave

In the plural, it changes only by adding -s:

• los problemas graves
• las situaciones graves

Not always. Parecer can be used in several ways.

For example:

• parece grave = seems serious
• parece difícil = seems difficult
• parece un error = seems like a mistake
• parece que llueve = it seems that it’s raining

So in your sentence, it is being used with an adjective, but it can also be followed by a noun or a whole clause.

No. In normal Spanish, you need the article here:

• El problema parece grave.

Spanish uses articles more regularly than English in many cases, and a singular countable noun like problema normally needs one unless something else is determining it.

So:

• el problema = the problem
• un problema = a problem

Without el or un, the sentence would sound incorrect here.