Ese comentario me parece exagerado.

Because me shows to whom it seems exaggerated.

A very literal breakdown is:

• Ese comentario = that comment
• me = to me
• parece = seems
• exagerado = exaggerated

So the structure is basically That comment seems exaggerated to me.

You can say Ese comentario parece exagerado, but then you are making a more general statement: That comment seems exaggerated. Adding me makes it explicitly your opinion.

Yes, in an important way.

Like gustar, parecer often uses an indirect object pronoun:

• me parece = it seems to me
• te parece = it seems to you
• le parece = it seems to him/her/you (formal)
• nos parece = it seems to us

So in Ese comentario me parece exagerado, the thing that seems is ese comentario, which is why the verb is parece (3rd person singular), not parezco or pareces.

Because the subject is Ese comentario, which is singular.

• Ese comentario me parece exagerado = singular subject
• Esos comentarios me parecen exagerados = plural subject

The verb agrees with the thing being judged, not with me.

Both are demonstratives, but they point to different levels of distance.

In Spain Spanish, a basic distinction is:

• este = this, something closer to the speaker
• ese = that, something a bit farther away, or already mentioned
• aquel = that over there, farther away or more distant

So ese comentario usually means that comment, often referring to a comment already mentioned in the conversation.

Because exagerado agrees with comentario, which is a masculine singular noun.

• comentario is masculine singular
• so the adjective is exagerado

Compare:

• Ese comentario me parece exagerado
• Esa crítica me parece exagerada

The adjective must match the noun in gender and number.

Here it is functioning as an adjective.

In Spanish, many past participles can also be used as adjectives. In this sentence, exagerado describes the noun comentario, so it behaves like an adjective meaning exaggerated or over the top.

They are similar, but not identical.

• Es exagerado = it is exaggerated
  This sounds more direct and objective.
• Me parece exagerado = it seems exaggerated to me
  This is softer and clearly marks it as your opinion.

Spanish often uses me parece to sound less blunt and more personal.

Yes. Spanish word order is flexible.

These are all possible:

• Ese comentario me parece exagerado
• A mí ese comentario me parece exagerado
• A mí me parece exagerado ese comentario

The most neutral version is the original one. Adding A mí gives emphasis: as for me / in my opinion.

Note that if you add A mí, you usually still keep me:

• A mí me parece...

No. It is an indirect object pronoun.

In me parece, me means to me, not me as a direct object.

So:

• me parece = seems to me
• te parece = seems to you
• le parece = seems to him/her

This is why many learners think of parecer as behaving similarly to gustar.

Yes, but the tone changes.

• Me parece exagerado = It seems exaggerated to me
• Creo que es exagerado = I think it is exaggerated
• Opino que es exagerado = I think / I am of the opinion that it is exaggerated

Me parece is often a bit more natural and less forceful in everyday conversation. Opino que can sound slightly more formal or deliberate.

Yes. Comentario is a masculine noun:

• el comentario
• ese comentario
• un comentario exagerado

Even though it ends in -o, which often signals masculine, you still have to learn noun gender individually. In this case, it is indeed masculine.

You would make the demonstrative, noun, verb, and adjective plural where needed:

• Esos comentarios me parecen exagerados.

Breakdown:

• esos = those
• comentarios = comments
• me parecen = seem to me
• exagerados = exaggerated

Everything agrees with the plural noun comentarios.

In standard Spain pronunciation, parece is approximately:

• pa-RE-the in much of Spain
  because c before e is pronounced like the th in thin

In Latin America, it is usually:

• pa-RE-se

The stress is on the middle syllable: re.