sono mise de ha, tyairoi pan yori kiiroi keeki no hou ga ninki desu.

No. Normal Japanese is usually written without spaces:

その店では、茶色いパンより黄色いケーキのほうが人気です。

The spaces in your sentence are just a learning aid to make the parts easier to see. Native Japanese writing does not normally separate words the way English does.

では is で + は.

• で marks the place where something applies or happens.
• は makes that place the topic or frame of the sentence.

So その店では means something like:

• at that store
• as for that store
• in that store, specifically

Using は gives it a topical or slightly contrastive feeling, as if you are talking about that store in particular.

This is a very common comparison pattern.

• Aより = than A
• Bのほうが = B is the one more...
• Cです = the quality being described

So:

茶色いパンより 黄色いケーキのほうが 人気です。

means:

Yellow cake is more popular than brown bread.

In other words:

• A = 茶色いパン
• B = 黄色いケーキ
• C = 人気

ほう literally means side, direction, or sometimes the one/option.

In comparisons, Bのほうが means something like:

• B is the one that...
• the B side is more...
• B rather than A

So 黄色いケーキのほうが does not mean possession. It is not like English cake’s side. It is a comparison structure meaning the yellow cake side / the yellow cake option.

This is why のほう is so common in Japanese comparisons.

Because 黄色いケーキのほう is the thing being described as 人気.

So the structure is:

• 茶色いパンより = than brown bread
• 黄色いケーキのほうが = yellow cake is the one that...
• 人気です = is popular

In this pattern, が often marks the item that wins the comparison or has the stronger quality.

Yes. In this sentence, both 茶色い and 黄色い are being used as -い adjectives:

• 茶色いパン = brown bread
• 黄色いケーキ = yellow cake

Many basic colors can be used this way, especially 赤い, 青い, 白い, 黒い, 黄色い.

茶色い is also used, although color words are a little mixed in Japanese, and some colors often appear with の instead.

Yes, in many contexts you can.

For color words, Japanese often allows either:

• Xい + noun
• Xの + noun

So you may hear things like:

• 茶色いパン
• 茶色のパン

Both can mean brown bread.

For 黄色, 黄色いケーキ is very natural. 黄色のケーキ can also appear, but 黄色い often feels more like the standard adjective form.

So the short answer is: yes, sometimes both are possible, but the most natural choice depends on the specific color word and expression.

人気 is basically a noun meaning popularity, but in sentences it often behaves like a na-adjective-type word:

• 人気だ
• 人気です

So:

黄色いケーキのほうが人気です。

means:

Yellow cake is more popular.

You can also see it before another noun as:

• 人気のケーキ = a popular cake

So it is not an -い adjective. You do not say 人気い.

Yes, sometimes you can say:

茶色いパンより黄色いケーキが人気です。

This is understandable and grammatical.

But のほうが makes the comparison clearer and more natural, especially when you are directly contrasting two things. It strongly signals:

• B rather than A
• B is the one that is more...

So in many everyday comparison sentences, のほうが sounds more explicit and more natural.

Often, yes.

その店では can sound like:

• at that store
• at that store, at least
• as for that store

This can imply a contrast such as:

• maybe not at other stores
• maybe in general things are different
• but in that store, this is true

The contrast may be strong or weak depending on context, but は often gives that kind of flavor.

A useful way to break it down is:

• その店では = as for that store
• 茶色いパンより = than brown bread
• 黄色いケーキのほうが = yellow cake is the one that...
• 人気です = is popular

So Japanese builds the sentence in this order:

1. set the topic or location
2. give the standard of comparison
3. give the item being favored
4. state the quality

That is why the Japanese order looks different from English, even though the meaning is the same.