Эта кепка новая, но мне кажется, что та старая была удобнее.

Because кепка is a feminine noun in Russian. The demonstrative этот / эта / это must agree with the noun in gender and number.

• этот = masculine
• эта = feminine
• это = neuter

So:

• эта кепка = this cap

The adjective also agrees:

• новая кепка = a new cap

That is why you get Эта кепка новая.

In Russian, the verb to be is normally omitted in the present tense.

So:

• Эта кепка новая literally looks like This cap new
• but it means This cap is new

This is completely normal in Russian.

Compare:

• Он дома = He is at home
• Она счастлива = She is happy
• Кепка новая = The cap is new

But in the past tense, Russian does use a form of to be, which is why later you see была.

Мне кажется literally means something like:

• it seems to me

The word мне is the dative case of я (I), because Russian expresses this idea as to me it seems.

So:

• мне кажется = it seems to me / I think / it seems
• тебе кажется = it seems to you
• ему кажется = it seems to him

This is a very common Russian way to soften an opinion. It often sounds less direct than a plain statement.

Что introduces the clause that follows, just like that in English.

So:

• мне кажется, что... = it seems to me that...

In this sentence:

• мне кажется, что та старая была удобнее
• it seems to me that that old one was more comfortable

In English, that is often optional. In Russian, что is very commonly used here.

Here кепка is understood and left out because it is obvious from context.

So та старая means:

• that old one
• more literally, that old [cap]

Russian often allows an adjective or demonstrative + adjective to stand in for a noun when the noun is already clear.

So the full idea is:

• та старая кепка была удобнее
• but Russian can shorten it to
• та старая была удобнее

This is very natural.

It can describe age, but in context it often means the old one / the previous one.

Since the sentence contrasts:

• Эта кепка новая = This cap is new
• та старая = that old one

the speaker is probably talking about:

• the current cap vs. the previous/older cap

So старая here is not just a random adjective; it helps identify which cap is meant.

There are two things happening here:

1. была is the past tense of быть (to be), feminine singular.
2. удобнее is the comparative form of удобный.

So:

• была = was
• удобнее = more comfortable / more convenient

Together:

• была удобнее = was more comfortable

It is feminine because the understood noun is кепка, which is feminine.

Russian often prefers the simple comparative form:

• удобный = comfortable
• удобнее = more comfortable

This is usually the most natural way to say it.

You can sometimes use более удобная, but it is usually less direct and often sounds more formal or heavier. In everyday speech, удобнее is the normal choice.

Also note that after была, the comparative form does not change for gender:

• кепка была удобнее
• пальто было удобнее
• стул был удобнее

Because the speaker is comparing:

• the cap now: Эта кепка новая = This cap is new
• the older cap in the past: та старая была удобнее = that old one was more comfortable

The new cap exists in the present situation, but the old cap is something the speaker had before, so Russian uses была.

This tense contrast is very natural:

• This one is new, but the old one was more comfortable.

Yes.

Russian uses commas here for two reasons:

1. Before но (but) joining two clauses:

   • Эта кепка новая, но...

2. Before что introducing a subordinate clause:

   • мне кажется, что...

So the punctuation is standard Russian punctuation.

Yes, Russian word order is flexible, but the original version is the most neutral and natural.

• Эта кепка новая, но мне кажется, что та старая была удобнее.

Russian word order can shift for emphasis, but not every rearrangement sounds equally natural. For a learner, it is best to treat this sentence as a good standard model:

• statement
• contrast with но
• opinion phrase мне кажется
• subordinate clause with что

So while Russian is flexible, this version is already the safest and most idiomatic one to use.