La tache d’humidité présente de la moisissure.

No. These are two different words:

• tache = stain, spot, mark
• tâche = task, job

In your sentence, la tache d’humidité means something like:

• the damp stain
• the moisture stain
• the water stain

So the sentence is talking about a mark on a wall, ceiling, etc., not a task.

Because French usually shortens de before a vowel sound.

• de + humidité → d’humidité

This is called elision.

Also, the h in humidité is a mute h, so it behaves like a vowel for this purpose. That is why you say:

• d’humidité
• not de humidité

Literally, it means the stain of humidity/moisture.

In more natural English, that would usually be:

• the damp patch
• the moisture stain
• the water stain

French often uses noun + de + noun where English might prefer an adjective:

• une tache d’humidité = a damp stain
• literally: a stain of moisture

Here, présente is a verb.

It is the third-person singular present form of présenter:

• je présente
• tu présentes
• il/elle présente

In this sentence, the subject is la tache d’humidité, which is singular, so the verb is présente.

Here présenter means something like:

• to show
• to display
• to have
• to exhibit

So La tache d’humidité présente de la moisissure means the damp stain shows/has mold.

That is a very good question, because this is a case where the French word is related to English present, but the usage is different.

In French, présenter can mean:

• to present
• to show
• to display
• to exhibit

In descriptions of damage, symptoms, or visible features, French often uses présenter where English would more naturally say:

• has
• shows
• is showing
• displays

So here, natural translations are:

• The damp stain has mold.
• The damp patch shows mold.
• The moisture stain is showing mold.

Because moisissure is usually treated as an uncountable noun here, like mold in English.

French commonly uses a partitive article with uncountable things:

• du
• de la
• de l’
• des

Since moisissure is feminine singular, you get:

• de la moisissure

This means some mold or simply mold.

So:

• présente de la moisissure = has/shows mold

Yes. That would also be very natural.

For example:

• Il y a de la moisissure sur la tache d’humidité.
• There is mold on the damp stain.

The difference is mainly one of style and focus:

• La tache d’humidité présente de la moisissure sounds a bit more formal, descriptive, or technical.
• Il y a de la moisissure... is more straightforward and conversational.

It is singular because the sentence is talking about one stain.

• la tache = the stain
• les taches = the stains

If it were plural, the verb would change too:

• Les taches d’humidité présentent de la moisissure.
• The damp stains have/show mold.

So the verb présente agrees with the singular subject la tache.

A simple pronunciation guide is:

la tash dy-mee-dee-tay pray-zahnt duh la mwah-zee-syur

A few helpful notes:

• tache sounds like tash
• humidité starts with a vowel sound because the h is mute
• présente has a nasal sound in -sen-: roughly pré-zahnt
• moisissure is pronounced roughly mwah-zee-syur

A more IPA-style version is:

[la taʃ dymidite pʁezɑ̃t də la mwazisyʁ]

Yes. Depending on context, everyday French might use something simpler, such as:

• La tache d’humidité a de la moisissure.
• The damp stain has mold.

or

• Il y a de la moisissure sur la tache d’humidité.
• There is mold on the damp stain.

The original sentence is perfectly correct, but présente sounds a little more formal, descriptive, or like something from a report or inspection note.