Després de treballar, la mare vol comprar roba.

Yes. Després by itself usually means afterwards or later:

• Treballa i després descansa. = He/She works and afterwards rests.

But when it is followed by a noun or a verb, Catalan normally uses després de:

• després de la feina = after work
• després de treballar = after working

So in your sentence, després de treballar is the normal way to say after working.

Because after després de, Catalan uses the infinitive, not the gerund.

English often says after working, with an -ing form. Catalan does not copy that structure here. It says:

• després de treballar
• després de menjar
• després d’estudiar

So treballar is correct because it is the infinitive.

Vol is the 3rd person singular present indicative of voler = to want.

So:

• jo vull = I want
• tu vols = you want
• ell/ella vol = he/she wants

In this sentence, la mare vol means the mother wants.

Because after voler, Catalan normally puts the second verb directly in the infinitive:

• vol comprar = wants to buy
• vol menjar = wants to eat
• volen marxar = they want to leave

English uses to before the second verb, but Catalan does not add anything here. So vol comprar is the normal structure, not vol de comprar or vol a comprar.

Catalan often uses the definite article with family members when talking about a specific person:

• la mare = the mother / my mother / mum, depending on context
• el pare = the father / my father / dad

English usually does not do this in the same way, so it can feel strange at first.

But when directly addressing the person, the article is usually dropped:

• Mare, escolta! = Mum, listen!

Here roba means clothes/clothing in general, not a specific set of clothes. In Catalan, it is very natural to leave out the article in that situation:

• comprar roba = to buy clothes

If you say la roba, you usually mean specific clothes already known from context, or sometimes the laundry/clothes as a definite thing:

• La roba és a l’armari. = The clothes are in the wardrobe.
• He de rentar la roba. = I have to wash the clothes / laundry.

So comprar roba is the right choice for buy clothes in a general sense.

Yes, roba is grammatically singular in Catalan when it means clothing/clothes as a general mass noun.

That means it behaves more like English clothing than like English clothes:

• molta roba = a lot of clothes
• aquesta roba és cara = these clothes / this clothing is expensive

So even though the English translation may use a plural word, Catalan uses singular grammar here.

Because Després de treballar is an introductory time expression placed at the beginning of the sentence. The comma helps separate that opening phrase from the main clause:

• Després de treballar, la mare vol comprar roba.

This is very natural in writing. You can also put the time phrase at the end:

• La mare vol comprar roba després de treballar.

That version has basically the same meaning, just a different word order.

Yes. That is completely natural.

Catalan is flexible with this kind of time phrase:

• Després de treballar, la mare vol comprar roba.
• La mare vol comprar roba després de treballar.

Both are correct. Putting després de treballar first gives it a little more emphasis as the setting or time frame. Putting it at the end is often a bit more neutral.