No trobo la talla que necessito, i per això em provaré l'abric gris demà.

No trobo means I can't find or I'm not finding.

• trobo = I find / am finding, from the verb trobar
• no makes it negative

So No trobo la talla... literally means I don’t find the size..., but in natural English we usually say I can’t find the size....

Talla means size, especially for clothing.

It is a feminine noun, so it takes the feminine article la:

• la talla
• not el talla

A learner may also see mida, which can also mean size, but talla is especially common for clothes.

Examples:

• Quina talla portes? = What size do you wear?
• No tenen la meva talla. = They don’t have my size.

que necessito is a relative clause describing la talla.

So:

• la talla = the size
• que necessito = that I need

Together:

• la talla que necessito = the size that I need

Here que means that / which.

English sometimes omits that, but Catalan keeps que:

• the size I need
• la talla que necessito

There is — it is que.

In this sentence, que is exactly the word linking la talla to necessito:

• la talla que necessito = the size that I need

Catalan uses que very often in relative clauses, much more consistently than English uses that.

per això means for that reason, because of that, or more naturally, that’s why.

In this sentence:

• No trobo la talla que necessito, i per això... means
• I can’t find the size I need, and that’s why...

It connects the first idea to the consequence in the second part.

Yes, depending on style.

Some alternatives are:

• per això = for that reason / that’s why
• així que = so
• per tant = therefore
• doncs = so / then

But per això works very naturally here because it clearly means because of that.

Because when talking about clothes, Catalan usually uses the pronominal form provar-se to mean to try on.

So:

• provar = to try / test
• provar-se = to try on

That is why the sentence has em:

• em provaré l'abric gris = I’ll try on the grey coat

Without em, provaré would sound more like I’ll test / try something, not specifically try on a garment.

em is the first-person singular weak pronoun, meaning roughly myself / to me, depending on the verb.

Here it is part of provar-se:

• em provaré = I will try on

It does not need a separate English translation word-for-word, because English expresses the whole idea with try on.

Compare:

• em rento = I wash myself / I wash
• em posaré l'abric = I’ll put on the coat
• em provaré l'abric = I’ll try on the coat

In Catalan, weak pronouns usually come before a conjugated verb.

So you get:

• em provaré
• la trobo
• no el vull

This is normal word order in Catalan.

Pronouns are attached after the verb mainly with:

• infinitives: provar-me
• gerunds: provant-me
• affirmative imperatives: prova't

But with a normal future form like provaré, the pronoun goes before:

• em provaré

Yes. provaré is the first-person singular simple future of provar.

So:

• provaré = I will try
• em provaré = I will try on

Because the sentence includes demà (tomorrow), the future tense fits very naturally.

Catalan could also sometimes use the near future with anar a in conversation, but the simple future is completely normal here.

Because abric begins with a vowel, and the masculine singular article el becomes l' before a vowel or silent h.

So:

• el llibre = the book
• l'abric = the coat
• l'hotel = the hotel

This is the same reason you see:

• l'amic
• l'escola
• l'home

Because in Catalan, adjectives often come after the noun.

So:

• l'abric gris = the grey coat
• la casa gran = the big house
• el cotxe vermell = the red car

English usually puts adjectives before the noun, but Catalan usually puts many descriptive adjectives after it.

demà means tomorrow, and placing it at the end is very natural in Catalan.

Catalan word order is flexible, but the end position often sounds smooth and neutral:

• Em provaré l'abric gris demà.

You could also move it for emphasis:

• Demà em provaré l'abric gris.

Both are correct, but the version with demà at the end sounds very ordinary and natural.

It is possible, but many writers would leave it out.

So you may see either:

• No trobo la talla que necessito i per això em provaré l'abric gris demà.
• No trobo la talla que necessito, i per això em provaré l'abric gris demà.

The comma can help mark the pause between the two clauses, especially because the second part explains a consequence. In everyday writing, punctuation here can vary a bit.

Yes. A few natural alternatives are possible, for example:

• No trobo la talla que necessito, així que demà em provaré l'abric gris.
• Com que no trobo la talla que necessito, demà em provaré l'abric gris.
• No trobo la meva talla, i per això demà em provaré l'abric gris.

These all keep a similar meaning, but the original sentence is perfectly understandable and grammatical.