Learn Hardcore Portuguese (Portugal): A minha irmã começou a desinfetar as mãos com álcool-gel sempre que entra em casa. - My sister started disinfecting her hands with hand sanitizer whenever she enters the house.

So a minha irmã is the most natural form in Portugal here.
You can say minha irmã without the article, but in European Portuguese that sounds more:

poetic/literary, or
like a vocative (when you address the person directly): Minha irmã, vem cá.

In everyday speech about someone (not to someone), a minha irmã is the default in Portugal.

What is the function of the a in começou a desinfetar?

Here a is a preposition that links the verb começar (to start) to another verb in the infinitive:

começar a fazer = to start doing
começar a estudar = to start studying
começar a desinfetar = to start disinfecting

Many Portuguese verbs require a specific preposition before another verb. Começar is normally followed by a when it has this meaning of starting an action.

Saying começou desinfetar (without a) is not standard; in European Portuguese you should include the a.

Why is it começou (past) but entra (present) in the same sentence?

The mix of tenses is deliberate and natural:

começou (past simple) – the habit began at some point in the past.
entra (present) – describes a repeated, current action: every time she comes in now.

So the idea is:

At some moment in the past she started this habit, and now, whenever she comes in, she does it.

If you made both verbs past (começou / entrou), it would sound like a single past event, not an ongoing habit:

A minha irmã começou a desinfetar as mãos com álcool-gel sempre que entrou em casa.
→ suggests only in the occasions when she entered back then, not necessarily now.

Using entra keeps the habit “alive” in the present.

Could I replace sempre que with quando? What’s the difference?

Yes, you could say:

…quando entra em casa.

Differences:

sempre que = whenever
Emphasises repetition: every single time.
quando = when / whenever
More neutral: can be one time or many times, context decides.

In this sentence, sempre que is slightly stronger and clearer for “every time she comes in”. Quando would still be correct, just a bit less explicit about the “always / every time” idea.

Why is it as mãos and not as suas mãos for “her hands”?

In Portuguese, with parts of the body, if the possessor is clear from the subject, we usually use the definite article, not a possessive:

Lavei as mãos. = I washed my hands.
Ele fechou os olhos. = He closed his eyes.
Ela cortou o cabelo. = She cut her hair.

So:

A minha irmã começou a desinfetar as mãos…
We already know we’re talking about my sister, so as mãos is understood as her hands.

As suas mãos is not wrong, but in this context it sounds more emphatic or contrastive, like stressing her as opposed to someone else’s hands.

Why is desinfetar not reflexive, like desinfetar-se?

Some Portuguese verbs can be either:

non‑reflexive: verb + direct object
reflexive: verb + -se

Here, desinfetar as mãos already has a clear direct object (as mãos), so you don’t need -se. The subject and the possessor of as mãos are already clear.

You might hear:

Ela desinfeta-se.
This is possible, but it’s less specific (it’s like she disinfects herself). It doesn’t explicitly say what she disinfects.

The most natural and precise here is the non-reflexive desinfetar as mãos.

What exactly is álcool-gel? Is the hyphen important?

Álcool-gel is what many English speakers call hand sanitiser or alcohol gel: a gel containing alcohol used to disinfect hands.

About the form:

It is normally written with a hyphen in European Portuguese: álcool-gel.
It is masculine: o álcool-gel.

In Brazil, people more often say álcool em gel (also masculine, and usually without hyphen because of the em).

So for Portugal:

desinfetar as mãos com álcool-gel = to disinfect (her) hands with hand sanitiser.

Why is it entra em casa and not entra na casa?

Both structures are possible, but they don’t mean exactly the same:

entrar em casa
→ “enter home / come into the house” in the sense of one’s own home or home in general. Very common:
Sempre que entro em casa, tiro os sapatos.
entrar na casa (em
- a casa)
  → “go into the house” as a specific building, not necessarily “home”. Often used when you’re talking about a particular house that has been mentioned:
  Entrámos na casa velha ao lado da igreja.

In this sentence, em casa expresses “at home, into the home” (her home), so entra em casa is the natural choice.

What’s the difference between em casa, a casa, para casa and em casa with article?

Key contrasts:

em casa
= at home / in(doors at) home
No article. Refers to the general idea of “home”, usually your own.
Estou em casa. = I’m at home.
para casa / a casa (direction)
= to home
Vou para casa. / Vou a casa. = I’m going home.
These talk about movement towards home.
na casa / em casa with article (na casa, à casa)
= in the / into the house (a specific house as a building)
Ela mora na casa azul. = She lives in the blue house.

In your sentence, we need the idea “whenever she comes into (her) home”, so entra em casa (no article) is ideal.

Could the time clause go first, like Sempre que entra em casa, a minha irmã começou…?

With this exact tense combination, no. The tenses would clash.

Sempre que entra em casa, … naturally invites a present habit in the main clause:
Sempre que entra em casa, a minha irmã desinfeta as mãos com álcool-gel.
= Whenever she comes in, my sister disinfects her hands… (present habit)

If you want to keep começou (past), it works best after the subject and before the infinitive clause, as in the original:

A minha irmã começou a desinfetar as mãos com álcool-gel sempre que entra em casa.

So:

Time clause first → main clause usually in the same “habitual” timeframe
Past começou
- present entra → keep the original order for natural flow.

Is there any difference between this European Portuguese sentence and how Brazilians would usually say it?

Core grammar is the same, but typical Brazilian choices might differ a bit in vocabulary:

In Brazil you’d very often hear:

Minha irmã começou a desinfetar as mãos com álcool em gel sempre que entra em casa.

Differences:

a minha irmã (Portugal) → minha irmã (Brazil)
Brazilians drop the article before possessives much more often, especially in everyday speech.
álcool-gel (Portugal) → álcool em gel (Brazil)
Both are understood; álcool em gel is more common in Brazil.

Tense use (começou / entra) and structures like sempre que, entrar em casa, as mãos are fine and natural in both varieties.

Could I change the tense to make it a simple present habit, like “My sister disinfects her hands every time she comes home”?

Yes. For a straightforward present habit in Portuguese, you’d say:

A minha irmã desinfeta as mãos com álcool-gel sempre que entra em casa.

Here:

desinfeta (present) = disinfects
entra (present) = comes in

This version doesn’t say when she started the habit; it only states that this is her current routine. The original with começou a desinfetar explicitly includes the idea that she started doing this at some point in the past.