La mampara está detrás del atril.

Spanish normally uses estar for location, so está is the correct choice here. A simple rule learners often use is: for where something is, use estar. So:

• La mampara está detrás del atril. = location
• La mampara es grande. = characteristic

Because detrás normally goes with de when you say what something is behind. So the full pattern is:

detrás de + noun

That gives you:

• detrás de la puerta
• detrás del atril
• detrás de mí

So detrás el atril is not correct.

Del is the contraction of de + el.

So:

• detrás de el atril becomes detrás del atril

This contraction is mandatory in normal Spanish. The only common exception is when el is part of a proper name, such as de El Escorial.

Because mampara is a feminine noun and atril is a masculine noun. In Spanish, nouns have grammatical gender, and the article must match:

• la mampara
• el atril

There is not always a logical reason from the meaning alone; it is just part of learning the noun. That said, mampara ends in -a, so feminine is not surprising. Atril ends in a consonant, so you simply have to learn that it is masculine.

Yes. Spanish allows some flexibility. You can also say:

Detrás del atril está la mampara.

That still means the same thing, but it puts more focus on the location. The original order, La mampara está detrás del atril, is the most neutral and straightforward.

The accent marks show the correct stress.

• está is stressed on the last syllable: es-TÁ
• detrás is stressed on the last syllable: de-TRÁS

Without the written accent, Spanish spelling rules would suggest a different stress pattern. So the accent marks are necessary.