Po przeprowadzce chcemy powiesić zasłonę w sypialni i dwa zdjęcia nad łóżkiem.

Because po in the sense of after requires the locative case.

• dictionary form: przeprowadzka = move / relocation
• locative singular: przeprowadzce

So po przeprowadzce means after the move or after moving.

Chcemy is the 1st person plural present form of chcieć:

• chcę = I want
• chcesz = you want
• chce = he/she/it wants
• chcemy = we want

So chcemy powiesić means we want to hang up.

This is a perfective vs. imperfective difference.

• powiesić = perfective, focuses on the completed result
• wieszać = imperfective, focuses on the process, repetition, or ongoing action

In this sentence, the idea is a planned task with a clear result: after moving, we want to get the curtain and pictures hung up. That is why powiesić sounds natural.

Because it is the direct object of powiesić, so it is in the accusative singular.

• nominative: zasłona
• accusative: zasłonę

This is very common with feminine nouns ending in -a:

• książka → książkę
• lampa → lampę
• zasłona → zasłonę

Because w meaning in takes the locative case when it describes location.

• dictionary form: sypialnia = bedroom
• locative singular: sypialni

So:

• w sypialni = in the bedroom

Because zdjęcie is a neuter noun.

With 2, Polish distinguishes:

• dwa for neuter and most non-feminine nouns
• dwie for feminine nouns

So:

• dwa zdjęcia
• but dwie lampy

After 2, 3, 4, Polish usually uses the nominative/accusative plural form of the noun.

• singular: zdjęcie
• plural: zdjęcia

So:

• dwa zdjęcia
• trzy zdjęcia
• cztery zdjęcia

But after 5+, the pattern changes:

• pięć zdjęć

This is one of the important number patterns in Polish.

Here it is accusative plural, because it is also a direct object of powiesić.

However, with inanimate nouns, the accusative plural often looks exactly the same as the nominative plural. So the form zdjęcia serves both roles.

In this sentence:

• zasłonę = direct object
• dwa zdjęcia = another direct object

Because nad here means above / over, and the noun is in the instrumental case.

• dictionary form: łóżko = bed
• instrumental singular: łóżkiem

So:

• nad łóżkiem = above the bed

This is a very common location pattern in Polish:

• nad stołem = above the table
• pod krzesłem = under the chair
• przed domem = in front of the house

In this sentence, Polish uses nad łóżkiem to describe the final location of the pictures: they will be hanging above the bed.

A learner may expect a motion-type form, but with powiesić Polish very naturally uses the location phrase nad łóżkiem. In other words, the sentence is focused on where the pictures will be once hung, not on the movement toward that place.

So nad łóżkiem is the normal choice here.

Because one verb can govern two coordinated objects.

So the structure is:

• powiesić zasłonę
• i dwa zdjęcia

This means:

• hang a curtain
• and two pictures/photos

Polish does not need to repeat the verb if the same verb applies to both things.

Yes. Polish word order is more flexible than English, because the cases show the grammatical roles.

The original sentence is neutral and natural:

• Po przeprowadzce chcemy powiesić zasłonę w sypialni i dwa zdjęcia nad łóżkiem.

Other orders are possible, but they change emphasis. For example, you could move w sypialni earlier to emphasize the room, or nad łóżkiem later or earlier depending on focus.

For learning purposes, the original version is a good standard model.

Usually zdjęcie most often means photo / photograph.

In a home sentence like this, dwa zdjęcia nad łóżkiem usually suggests two photos hanging above the bed, often framed.

If you specifically meant paintings or art pictures, Polish might use obrazy instead.