El suelo está húmedo después de la lluvia.

Because estar is used for a condition or state, especially one that can change. In El suelo está húmedo, the ground is damp right now, as a result of the rain.

If you used es húmedo, it would suggest that the ground is inherently or generally damp, which is not the idea here.

A useful shortcut:

• ser = what something is
• estar = how something is

Here, suelo means ground or floor surface.

In this sentence, because it mentions rain, el suelo is best understood as the ground.

Be careful: suelo can also mean floor indoors:

• El suelo de la cocina está sucio = The kitchen floor is dirty.

So the word is broader than English ground.

In Spanish, common nouns often take an article where English would not. So después de la lluvia is the normal way to say after the rain.

Después de lluvia sounds incomplete or unnatural in standard Spanish in this context.

This is a common difference from English:

• después de la cena = after dinner
• después de la tormenta = after the storm
• después de la lluvia = after the rain

Because después normally needs de before a noun.

So:

• después de la lluvia = after the rain
• después de comer = after eating

If después appears alone, it usually means afterwards:

• Llovió y después salió el sol = It rained and afterwards the sun came out.

Both can relate to wetness, but they are not exactly the same.

• húmedo = damp, humid, slightly wet
• mojado = wet, usually more directly or noticeably wet

So El suelo está húmedo suggests the ground is damp after the rain, not necessarily soaking wet.

Compare:

• La toalla está mojada = The towel is wet
• El ambiente está húmedo = The air is humid / damp
• El suelo está húmedo = The ground is damp

Because it is a masculine singular adjective agreeing with suelo, which is a masculine singular noun.

Agreement here is:

• el suelo = masculine singular
• húmedo = masculine singular

Other forms would be:

• la tierra está húmeda = the ground/soil is damp
• los suelos están húmedos = the floors/grounds are damp
• las calles están húmedas = the streets are damp

Good question, because suelo can also mean I usually as a verb form of soler:

• Suelo estudiar por la noche = I usually study at night

But in this sentence, it is clearly a noun because:

• it has the article el
• it is followed by está húmedo, which describes the ground

So El suelo = the ground, not I usually.

It is pronounced approximately OO-meh-dho in Spain.

A few points:

• the h is silent
• the stress falls on the first syllable: HÚ-me-do
• the written accent mark shows that stress

It has an accent because it is an esdrújula word, meaning the stress falls on the third-to-last syllable. In Spanish, all esdrújulas take a written accent.

In most of Spain, lluvia is pronounced roughly like YOO-bya.

More precisely:

• ll is usually pronounced like y in modern Spanish
• v/b in Spanish are pronounced very similarly
• the stress is on the first syllable: LLU-via

Depending on the speaker or region, the exact sound of ll can vary a little, but for most learners, treating it like y is a good approach.

Yes. Tras la lluvia is correct and means the same thing: after the rain.

The difference is mostly stylistic:

• después de la lluvia = more neutral and everyday
• tras la lluvia = slightly more literary or formal in some contexts

For a learner, después de la lluvia is the safest and most common choice.

Sometimes, but not always.

• suelo refers to the ground surface, the floor, or the land underfoot
• tierra often means earth, soil, or land

In this sentence, el suelo está húmedo sounds very natural for the ground is damp.

If you say la tierra está húmeda, that sounds more like the soil is damp, which is slightly more specific.

So both can work, but they are not perfect synonyms.