bunbetuhyou ni yoru to, akikan to kosi ha sigengomi desu.

Here, によると means according to.

So 分別表によると means according to the sorting chart.

Even though よる has other uses in Japanese, in this pattern it is best learned as a set expression:

• N によると = according to N

A very similar expression is N によれば, which also means according to N.

In N によると, the に marks the source or basis of the information.

So:

• 分別表によると = according to the sorting chart

This is just how the expression is built. It is not something you would usually translate piece by piece in natural English. For learners, it is easiest to remember によると as one chunk.

No, the two と's are doing different jobs.

1. In によると, the と is part of the fixed expression Nによると = according to N.
2. In 空き缶と古紙, the と is the normal particle meaning and, joining two nouns.

So:

• 分別表によると = according to the sorting chart
• 空き缶と古紙 = empty cans and waste paper

Same sound, different function.

Because 空き缶と古紙 is the topic of the sentence.

The structure is:

• X は Y です = As for X, it is Y.

Here, the topic is actually a combined noun phrase:

• 空き缶と古紙は = as for empty cans and waste paper

Then the sentence tells you how they are classified:

• 資源ごみです = are recyclable garbage / recyclables

So the whole sentence is basically:

• As for empty cans and waste paper, they are recyclable garbage.

Yes. In 空き缶と古紙は, the は applies to the whole phrase 空き缶と古紙.

This is very common in Japanese. You can think of it as:

• [X and Y] are Z

So:

• 空き缶と古紙は資源ごみです = Empty cans and waste paper are recyclable garbage.

You do not need to put は on each noun separately.

Because 資源ごみ is the predicate noun, and です is the copula.

This is the standard pattern:

• A は B です = A is B

So here:

• 空き缶と古紙は = empty cans and waste paper
• 資源ごみです = are recyclable garbage

No extra particle is needed between 資源ごみ and です.

Using は makes 空き缶と古紙 the topic and presents a classification or general statement.

So the sentence feels like:

• As for empty cans and waste paper, they are recyclables.

If you used が, the nuance would shift. が often marks the grammatical subject more directly and can sound more like introducing new information or answering a specific question.

For a labeling or classification statement like this, は is very natural.

Japanese nouns usually do not show singular vs. plural the way English nouns do.

So:

• 空き缶 can mean an empty can or empty cans
• 古紙 can mean waste paper in a general sense

In a garbage-sorting sentence like this, they are understood generically, so English often translates them as plurals:

• empty cans and waste paper

分別表 is a compound noun:

• 分別 = sorting, separating into categories
• 表 = chart, table, list

So 分別表 means something like:

• sorting chart
• separation chart
• garbage sorting guide

In this sentence, it refers to a chart that tells you how different trash items should be sorted.

Literally, yes:

• 古 = old
• 紙 = paper

But in real usage, especially in recycling and trash-sorting contexts, 古紙 means waste paper or paper for recycling.

It usually refers to things like:

• newspapers
• magazines
• cardboard
• paper packaging

So it does not mean ancient paper or old documents in a historical sense here.

資源ごみ means garbage that can be reused or recycled as a resource.

It is often translated as:

• recyclable garbage
• recyclables
• resource waste

The parts are:

• 資源 = resource
• ごみ = garbage, trash

In everyday English, recyclables is often the most natural translation.

Yes. It ends with です, which makes it polite.

The plain form would be:

• 分別表によると、空き缶と古紙は資源ごみだ。

The meaning is the same, but です is the standard polite form and is very common in explanations, notices, and educational material.

No. Standard Japanese is normally written without spaces between words.

So this sentence would usually appear as:

• 分別表によると、空き缶と古紙は資源ごみです。

Spaces are often added only in beginner materials to make the sentence easier to read.

You could, but the nuance is different.

• 分別表によると = according to the sorting chart
• 分別表では = in the sorting chart / as for the sorting chart

によると clearly emphasizes the source of information.
That makes it especially natural here, because the sentence is telling you what the chart says.

So 分別表によると is the best choice if you want to say according to the sorting chart.