Im Bad stehen noch zwei Rollen Toilettenpapier neben dem neuen Duschgel.

Im is a contraction of in dem.

• in = in
• dem = the dative form of das

So:

• im Bad = in dem Bad = in the bathroom

In everyday German, contractions like im, am, zum, and beim are very common.

Because Bad is a noun, and all nouns in German are capitalized.

Here, das Bad means bathroom or bath. In this sentence, it means bathroom.

So:

• das Bad = the bathroom
• im Bad = in the bathroom

German often puts a location or another important piece of information first.

The key rule is that the finite verb must still stay in second position.

So the structure is:

• Im Bad = position 1
• stehen = position 2
• noch zwei Rollen Toilettenpapier = the rest

That is why you get:

• Im Bad stehen noch zwei Rollen Toilettenpapier ...

and not:

• Im Bad noch zwei Rollen Toilettenpapier stehen ...

You could also say:

• Noch zwei Rollen Toilettenpapier stehen im Bad neben dem neuen Duschgel.

That is also grammatical, but it places the emphasis differently.

In German, objects are often described with verbs that show their position:

• stehen = stand
• liegen = lie
• hängen = hang

German prefers this kind of verb more often than English does.

Here, Toilettenpapierrollen are imagined as being upright or placed in a standing position, so stehen is natural.

So:

• Im Bad sind noch zwei Rollen Toilettenpapier = possible, but less vivid
• Im Bad stehen noch zwei Rollen Toilettenpapier = more natural and descriptive

Because the subject is plural:

• zwei Rollen = two rolls

Since there are two rolls, the verb must also be plural:

• eine Rolle steht = one roll stands
• zwei Rollen stehen = two rolls stand

So stehen agrees with zwei Rollen.

Noch can have several meanings, but here it most likely means something like:

• still
• also
• yet
• in addition

In this sentence, it suggests that the two rolls of toilet paper are still there or there as well.

Depending on context, the sentence could imply:

• There are still two rolls left in the bathroom.
• There are also two rolls in the bathroom, besides other things.
• There are yet another two rolls there.

So noch adds a small nuance rather than changing the basic meaning completely.

Because Toilettenpapier is normally an uncountable material noun, like water or paper in English.

You usually do not count the material itself directly. Instead, you count the units:

• eine Rolle Toilettenpapier = a roll of toilet paper
• zwei Rollen Toilettenpapier = two rolls of toilet paper

This works just like English:

• not usually two toilet papers
• but two rolls of toilet paper

Because Toilettenpapier is being used as a material noun after a measure word:

• zwei Rollen Toilettenpapier

This is like English:

• two bottles water would be wrong in English
• but two bottles of water is correct

German often does this without an extra article:

• eine Tasse Kaffee = a cup of coffee
• ein Glas Milch = a glass of milk
• zwei Rollen Toilettenpapier = two rolls of toilet paper

You would not normally say:

• zwei Rollen des Toilettenpapiers

unless you meant a very specific toilet paper already known in the context.

Because neben is a two-way preposition. That means it can take either:

• accusative for movement toward something
• dative for location

Here there is no movement. The toilet paper is located next to the shower gel. So German uses the dative.

• neben dem neuen Duschgel = next to the new shower gel

If there were movement, you would use accusative:

• Ich stelle das Toilettenpapier neben das neue Duschgel. = I put the toilet paper next to the new shower gel.

This is because of dative singular neuter.

The noun is:

• das Duschgel = the shower gel

After neben in a location sense, it becomes dative:

• dem Duschgel

The adjective neu- must also take the correct ending in the dative singular after dem:

• dem neuen Duschgel

So the parts are:

• dem = dative singular neuter article
• neuen = adjective ending for that form
• Duschgel = noun

Yes, the standard noun is:

• das Duschgel

So its forms are:

• das neue Duschgel = nominative/accusative
• dem neuen Duschgel = dative

Many German compound nouns take the gender of the last part. Here the last part is Gel, and das Gel is neuter, so das Duschgel is neuter too.

Yes. Both are possible.

• das Bad often means bathroom
• das Badezimmer also means bathroom, and is a bit more explicit

So these are both fine:

• Im Bad stehen noch zwei Rollen Toilettenpapier ...
• Im Badezimmer stehen noch zwei Rollen Toilettenpapier ...

Im Bad is very common and natural in everyday German.

Sometimes yes, but it changes the image.

• stehen suggests the rolls are upright
• liegen suggests they are lying flat

So both can be grammatical, depending on the situation:

• Im Bad stehen noch zwei Rollen Toilettenpapier ...
• Im Bad liegen noch zwei Rollen Toilettenpapier ...

German often chooses the verb based on the physical orientation of the object. English usually just says there are.