Le palier du premier étage est sombre, mais celui du rez-de-chaussée est très propre.

Palier usually means a landing: the small area at the top of a staircase, often giving access to rooms or apartments on that level.

So it is not the whole floor of the building. It is the shared space around the stairs/elevator on that level.

Because du is the contraction of de + le.

• de le premier étage → du premier étage
• de le rez-de-chaussée → du rez-de-chaussée

Here, de shows a relationship like of or on/from that level:

• le palier du premier étage = the landing of/on the first floor
• celui du rez-de-chaussée = the one on the ground floor

Celui means the one. It avoids repeating le palier.

So instead of saying:

• Le palier du premier étage est sombre, mais le palier du rez-de-chaussée est très propre

French uses the smoother version:

• Le palier du premier étage est sombre, mais celui du rez-de-chaussée est très propre

This is very common in French.

Because celui replaces le palier, and palier is:

• masculine
• singular

The matching demonstrative pronouns are:

• celui = masculine singular
• celle = feminine singular
• ceux = masculine plural
• celles = feminine plural

Since palier is masculine singular, celui is the correct form.

French uses definite articles more often than English does.

In this sentence:

• le palier = the landing
• le premier étage = the first floor
• le rez-de-chaussée = the ground floor

Even where English might sometimes sound more natural without repeating the, French normally keeps the article.

Be careful: this depends on the variety of English.

In French:

• rez-de-chaussée = ground floor
• premier étage = the floor above the ground floor

So:

• in British English, premier étage often corresponds to first floor
• in American English, it often corresponds to second floor

This is a very common source of confusion.

They agree with the noun they describe, which is palier.

Since palier is masculine singular, the adjectives are also masculine singular:

• sombre = masculine/feminine singular form
• propre = masculine/feminine singular form

These two adjectives happen to have the same form in masculine and feminine singular, so you do not see a visible change here.

Because they are being used as predicate adjectives, not directly before the noun.

French can describe something in two main ways:

• un palier sombre = a dark landing
• le palier est sombre = the landing is dark

In your sentence, the structure is:

• subject + être + adjective

So:

• Le palier ... est sombre
• celui ... est très propre

Literally, rez-de-chaussée comes from an older expression meaning something like level with the roadway/ground.

For a learner, the important thing is simply:

• rez-de-chaussée = ground floor

It is a fixed expression, so it is best learned as one vocabulary item.

Yes. This would also be correct:

• Le palier du premier étage est sombre, mais le palier du rez-de-chaussée est très propre.

But using celui is more natural because it avoids repetition.

So:

• repeated noun = correct, but heavier
• celui = more elegant and more typical

Très means very and simply intensifies propre.

• est sombre = is dark
• est très propre = is very clean

There is no special grammar rule here saying one adjective must have très and the other must not. The speaker just chose to make propre stronger.

You could also say:

• est très sombre
• est propre

if that matched the meaning you wanted.