Эта ткань почти не мнётся, и это очень удобно в дороге.

Because ткань is a feminine noun, so the demonstrative must also be feminine:

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

So эта ткань is the correct nominative singular form.

In Russian, nouns ending in -ь can be either masculine or feminine, so the soft sign alone does not tell you the gender.

Ткань is one of the feminine nouns of the so-called third declension. Learners usually just have to memorize the gender of each -ь noun.

That matters because it affects agreement:

• эта ткань
• новая ткань
• ткань мнётся

Почти не means almost not, which in natural English is often hardly or doesn’t really.

So the idea is:

• почти не мнётся = hardly wrinkles / almost doesn’t crease

It softens the statement. It does not mean the fabric can never wrinkle; it means it wrinkles very little.

Мнётся is the 3rd person singular present form of мяться.

Why 3rd person singular?

Because the subject is эта ткань, which is singular:

• ткань мнётся = the fabric wrinkles / gets creased

The verb is singular because ткань is singular.

The non-reflexive verb is мять, which means to crumple / wrinkle / crush something.

• мять ткань = to crumple the fabric

The reflexive/intransitive form мяться means that the thing itself gets wrinkled / creased:

• ткань мнётся = the fabric wrinkles easily / gets creased

So -ся here helps turn the idea from doing something to an object into what happens to the object itself.

A rough learner-friendly pronunciation is mnyót-sa.

A few important points:

• ё is always stressed
• -тся in this form is pronounced roughly like -ца / -tsa
• the beginning мн- can feel awkward for English speakers, but both sounds are there

So although it is written мнётся, it sounds approximately like mnyótsa.

The second это does not mean the same thing as эта in эта ткань.

Here, это refers to the whole previous idea:

• This fabric hardly wrinkles
• and that / this fact is very convenient when traveling

So это here is like that, this, or the fact that...

It points to the situation, not directly to the noun ткань.

Because удобно here is not describing the noun ткань directly.

Compare:

• удобная ткань = a convenient fabric
  (adjective agreeing with ткань)
• это удобно = this is convenient
  (predicative form, describing a situation)

In the sentence это очень удобно в дороге, Russian is evaluating the situation: the fact that the fabric hardly wrinkles is convenient.

That is why удобно is used.

В дороге uses the prepositional case:

• дорога → в дороге

After в, Russian often uses the prepositional case when meaning in / during / while in something.

Here в дороге is an idiomatic expression meaning:

• while traveling
• on a trip
• when on the road

It does not literally mean standing physically on a road.

Because на дороге usually means on the road in a literal physical sense:

• Машина стоит на дороге = The car is standing on the road

But в дороге usually means during travel or while on a journey:

• Это удобно в дороге = This is convenient when traveling

So в дороге is the natural choice here.

Russian normally omits the present-tense form of to be.

So:

• это очень удобно literally looks like this very convenient
• but it means this is very convenient

This is completely normal in Russian. You usually do not say есть for present-tense is/are in sentences like this.

Because и is joining two full clauses:

1. Эта ткань почти не мнётся
2. это очень удобно в дороге

Each part has its own grammatical center, so Russian uses a comma before и here.

If и joined only two words or two simple parts of one clause, there might be no comma, but here the comma is correct.

Yes. Russian word order is flexible, although the original order is natural and neutral.

For example, you could also say:

• Эта ткань почти не мнётся, и в дороге это очень удобно.

That puts a bit more emphasis on в дороге.

The original sentence is good because it flows naturally:

• first: the property of the fabric
• then: why that matters

So the given word order is probably the most straightforward one for everyday use.