Cuando llego a casa, me quito las botas y me pongo las pantuflas.

Because the sentence describes a habitual action: something the speaker typically does whenever they get home.

• llego = I arrive / I get home in the present tense
• In Spanish, the present tense is often used for routines and general habits.

So Cuando llego a casa... means When I get home... / Whenever I get home...

By contrast:

• cuando llegué a casa = when I got home (one specific past occasion)
• cuando llegaré a casa is not natural here; for the future, Spanish usually says cuando llegue a casa

Because this sentence talks about something that happens regularly or whenever the situation occurs.

In Spanish:

• Cuando + present tense is common for habitual actions
• Cuando + present subjunctive is common for future events

So:

• Cuando llego a casa, me quito las botas...
  = When/Whenever I get home, I take off my boots...
  habitual

• Cuando llegue a casa, me quitaré las botas...
  = When I get home, I’ll take off my boots...
  future

That contrast is very important in Spanish.

In Spanish, casa often appears without an article when it means home in a general sense.

So:

• llegar a casa = to get home
• estar en casa = to be at home
• ir a casa = to go home

But la casa is used when you mean the house as a physical building or a specific house:

• Llegué a la casa de Ana. = I arrived at Ana’s house.

So in your sentence, a casa means home, not to the house.

They are reflexive because the subject is doing the action to themselves.

• quitar = to remove / take away

• quitarse = to take off something from oneself

• poner = to put / place
• ponerse = to put on clothing, shoes, accessories, etc.

So:

• me quito las botas = I take off my boots
• me pongo las pantuflas = I put on my slippers

The me shows that the person both performs the action and is affected by it.

This is a very common Spanish pattern. With clothing, body parts, and personal items, Spanish often uses the definite article instead of a possessive when it is already clear whose items they are.

So Spanish prefers:

• me quito las botas
• me pongo las pantuflas

rather than:

• me quito mis botas
• me pongo mis pantuflas

The reflexive pronoun me already tells you the boots and slippers belong to the speaker.

Using mis is possible in some contexts, but it often sounds more emphatic, contrastive, or less natural in ordinary situations.

Usually, no—not with this meaning.

• quitar las botas means to remove the boots, possibly from someone or something else
• quitarse las botas means to take off one’s own boots

For example:

• Le quito las botas al niño. = I take the child’s boots off.
• Me quito las botas. = I take off my boots.

So in your sentence, me is important because the speaker is removing their own boots.

The difference is very similar:

• poner = to put / place something somewhere
• ponerse = to put on something oneself, especially clothes or footwear

Examples:

• Pongo las llaves en la mesa. = I put the keys on the table.
• Me pongo el abrigo. = I put on my coat.

So:

• me pongo las pantuflas = I put on my slippers not
• pongo las pantuflas, which would usually mean I place the slippers somewhere.

Because Spanish often omits subject pronouns when the verb ending already shows who the subject is.

• llego clearly means I arrive
• me quito clearly means I take off
• me pongo clearly means I put on

So yo is unnecessary unless you want emphasis or contrast:

• Yo llego a casa y me quito las botas.
  This could sound like I get home and take off my boots, maybe contrasting with someone else.

Normally, Spanish sounds more natural without yo.

The comma separates the time clause from the main clause.

• Cuando llego a casa = introductory clause
• me quito las botas y me pongo las pantuflas = main clause

In English, we usually do the same:

• When I get home, I take off my boots and put on my slippers.

So the comma here is natural and standard.

Pantuflas means slippers, and it is understood, but in Spain many speakers more commonly say:

• zapatillas
• zapatillas de casa

depending on the region and context.

So your sentence is correct, but a learner of Spanish from Spain should know that in everyday Peninsular Spanish, zapatillas de casa may sound more common than pantuflas.

Examples:

• Me pongo las zapatillas de casa.
• Me quito las botas y me pongo las zapatillas.

Because each reflexive verb needs its own reflexive pronoun.

So you need:

• me quito
• me pongo

Each verb has to be complete on its own.

That is why Spanish says:

• me quito las botas y me pongo las pantuflas

and not:

• me quito las botas y pongo las pantuflas

Without the second me, the second verb would mean I place the slippers, not I put them on.

Yes. In this sentence, cuando can naturally be understood as either:

• when I get home or
• whenever I get home

Because the whole sentence is in the present tense and describes a routine, English often uses whenever to bring out the habitual meaning more clearly.

So the Spanish sentence can express:

• a regular pattern
• something that happens every time the situation occurs

Yes. Al + infinitive is another very common way to express when/on doing something.

So you could say:

• Al llegar a casa, me quito las botas y me pongo las pantuflas.

This means roughly:

• On arriving home, I take off my boots and put on my slippers.
• When I get home, I take off my boots and put on my slippers.

Both are correct, but they feel slightly different:

• Cuando llego a casa... emphasizes a repeated situation more directly
• Al llegar a casa... is a very natural alternative and can sound a bit more compact

Sometimes, but the meaning changes slightly.

• llegar a casa = to arrive/get home
• volver a casa = to return/go back home

So:

• Cuando llego a casa... focuses on the moment of arriving
• Cuando vuelvo a casa... focuses more on returning home from somewhere

In many contexts both work, but llego a casa is the closer match for when I get home.

Yes—several very typical Spanish features appear here:

1. Subject pronouns are omitted

   • llego, not usually yo llego

2. Reflexive verbs are used for dressing actions

   • me quito, me pongo

3. Definite articles replace possessives with clothing

   • las botas, las pantuflas, not usually mis

4. Present tense expresses habit

   • Cuando llego a casa...

So even though the sentence is simple, it contains several patterns that are extremely common and useful in everyday Spanish.