La guia diu que aquest quadre és una pintura de la ciutat, i a mi m'agrada molt.

Yes. Guia can mean:

• guide as a person
• guidebook as a thing

So la guia could be either the female guide or the guidebook, depending on context.

If you want to say the male guide, that would be el guia.

In this sentence, both interpretations are grammatically possible, because both a person and a guidebook can say something.

Diu is the 3rd person singular present form of dir, which means to say.

The subject is la guia, which is singular, so you use diu:

• jo dic = I say
• tu dius = you say
• ell/ella diu = he/she says
• nosaltres diem = we say
• vosaltres dieu = you all say
• ells/elles diuen = they say

So La guia diu... means The guide says...

Here que introduces a subordinate clause, just like that in English:

• La guia diu que... = The guide says that...

In English, that is often optional:

• The guide says this painting...
• The guide says that this painting...

In Catalan, que is normally kept after verbs like dir.

Because quadre is a masculine singular noun, so the demonstrative must match it:

• aquest = this, masculine singular
• aquesta = this, feminine singular
• aquests = these, masculine plural
• aquestes = these, feminine plural

So:

• aquest quadre = this painting / this picture
• aquesta pintura = this painting

The form changes to agree with the noun.

This is a very natural question, because the sentence uses both.

• quadre usually means a painting, picture, or framed artwork as an object
• pintura means painting as an art form, a painting as a type of work, or even paint in other contexts

So aquest quadre focuses on the artwork as an object in front of you, while una pintura de la ciutat classifies what kind of artwork it is.

A rough nuance is:

• quadre = the piece on the wall
• pintura = a painting rather than, for example, a photo or drawing

In Catalan, de is commonly used to mean of when talking about what an artwork depicts:

• una foto de la ciutat = a photo of the city
• un dibuix de la ciutat = a drawing of the city
• una pintura de la ciutat = a painting of the city

Here de la ciutat tells you what the painting shows.

If you said sobre la ciutat, that would sound more like about the city or concerning the city, which is a different idea.

With agradar, Catalan often uses a + person:

• A mi m'agrada = I like it
• literally, something like To me, it is pleasing

So a mi means to me.

It can be used:

• for emphasis
• for contrast
• for clarity

In this sentence, a mi adds a personal emphasis: as for me, I like it a lot.

Because jo is a subject pronoun, but here Catalan uses a prepositional phrase with a:

• jo = I
• a mi = to me

Since agradar takes this to someone structure, a mi is the correct form.

So:

• Jo dic... = I say...
• A mi m'agrada... = I like...

They are different structures.

Yes, in a way they both point to to me, and this is very normal in Catalan.

• m' is the unstressed object pronoun
• a mi is the stressed form

This kind of doubling is extremely common, especially with agradar and similar verbs.

So:

• M'agrada molt = I like it a lot
• A mi m'agrada molt = I like it a lot / Me, I like it a lot

The version with a mi is more emphatic or contrastive.

Because agradar does not work like English to like.

In Catalan, agradar works more like to please:

• Aquest quadre m'agrada
  literally: This painting pleases me

So the verb agrees with the thing that is pleasing, not with the person who feels the liking.

Here the thing liked is singular, so you get:

• agrada = singular

Compare:

• M'agrada aquest quadre = I like this painting
• M'agraden aquests quadres = I like these paintings

So it is m'agrada, not m'agrado.

Because the full form is em agrada, and em contracts before a vowel:

• em agrada → m'agrada

This is very common with Catalan clitic pronouns:

• em escolta → m'escolta
• et agrada → t'agrada

So m'agrada is just the normal contracted form of em agrada.

Yes. That would be perfectly correct.

• M'agrada molt = I like it a lot
• A mi m'agrada molt = I like it a lot / As for me, I like it a lot

Including a mi gives extra emphasis, but it is not required.

Because molt here modifies the verb phrase m'agrada and means a lot or very much.

In neutral Catalan word order, it normally comes after the verb:

• m'agrada molt = I like it a lot

That is the most natural placement in this sentence.

Not really necessary, but it can be acceptable.

Catalan usually does not put a comma before i when simply joining elements. However, a comma may appear when:

• there is a pause
• two full clauses are being linked
• the writer wants extra clarity

So both of these can be acceptable:

• La guia diu que aquest quadre és una pintura de la ciutat i a mi m'agrada molt.
• La guia diu que aquest quadre és una pintura de la ciutat, i a mi m'agrada molt.

The version without the comma is often the more neutral one.