Когда идёт дождь, мой сын любит мастерить из картона и цветной бумаги дома.

Because идёт дождь is the normal Russian way to say it is raining.

Russian often uses идти in weather expressions:

• идёт дождь = it is raining
• идёт снег = it is snowing

Literally, идти usually means to go / to be going, but in these expressions it has a special idiomatic meaning. This is just the standard pattern Russian uses.

Russian does not use a dummy subject like English it in weather expressions.

In English, it in it is raining does not really refer to anything. Russian simply does not need that kind of placeholder. Instead, the sentence is built around the weather noun itself:

• дождь = rain

So in идёт дождь, дождь is the grammatical subject.

Russian present tense is often used for habitual or repeated situations, just like English:

• Когда идёт дождь... = When it rains...

It does not have to mean only right now. Here it means whenever rain is falling / in rainy weather.

If you wanted a one-time future meaning, Russian would often use something different, for example:

• Когда пойдёт дождь... = When it starts raining / when the rain begins

So идёт here fits the general, repeated meaning very well.

Because Когда идёт дождь is a subordinate clause introduced by когда.

Russian normally separates this kind of clause with a comma:

• Когда идёт дождь, мой сын любит...

This is similar to English:

• When it rains, my son likes...

If you reverse the order, you still use a comma:

• Мой сын любит мастерить дома, когда идёт дождь.

After любить, Russian commonly uses the infinitive to say that someone likes doing something:

• любить читать = to like reading
• любить плавать = to like swimming
• любить мастерить = to like making/crafting things

So мой сын любит мастерить means my son likes to make/craft things.

This is very natural Russian.

Делать is the general verb to do / to make.

Мастерить is more specific. It usually suggests:

• making something by hand
• crafting
• building small things
• tinkering

So мастерить is a very good choice for making things out of cardboard and colored paper. It sounds more like crafting than just making.

Because the preposition из usually requires the genitive case when it means out of / from a material.

So:

• картон → картона
• цветная бумага → цветной бумаги

That is why the sentence says:

• из картона и цветной бумаги = out of cardboard and colored paper

This is a very common pattern in Russian:

• из дерева = out of wood
• из бумаги = out of paper
• из пластика = out of plastic

Because the whole phrase is in the genitive after из.

The basic form is:

• цветная бумага = colored paper

But after из, both the adjective and noun change:

• цветная → цветной
• бумага → бумаги

So:

• из цветной бумаги = out of colored paper

This is adjective-noun agreement in the required case.

Дома here means at home.

This is a very common adverb in Russian:

• Я дома. = I am at home.
• Он работает дома. = He works at home.

В доме usually means in the house/building, focusing more on the physical building itself.

So in this sentence, дома is more natural if the idea is simply that the son does crafts at home.

Yes. Russian word order is fairly flexible, and changing it usually changes emphasis more than basic meaning.

For example, you could also say:

• Когда идёт дождь, мой сын любит дома мастерить из картона и цветной бумаги.
• Мой сын любит мастерить из картона и цветной бумаги дома, когда идёт дождь.
• Мой сын любит дома мастерить из картона и цветной бумаги, когда идёт дождь.

The original sentence is perfectly natural. In it, дома most naturally goes with мастерить, meaning that the crafting happens at home.