mainanbaakaado to zairyuukaado wo tukau.

Here, と connects two nouns and means and.

So:

マイナンバーカード と 在留カード
= My Number card and residence card

This is one of the most common uses of と. It joins nouns in a complete list.

Yes. と can also mean with, but in this sentence it is clearly the and use.

Compare:

友だちと行く = go with a friend
りんごとバナナ = apples and bananas

In マイナンバーカード と 在留カード を 使う, both words before と are objects being used, so and is the natural interpretation.

Because the two nouns are joined into one combined object phrase:

マイナンバーカード と 在留カード = the My Number card and residence card

Then を marks that whole phrase as the direct object of 使う.

So the structure is:

[マイナンバーカード と 在留カード] を 使う
= use [the My Number card and residence card]

You do not normally need:

マイナンバーカードを 在留カードを 使う

That would be incorrect here.

Because Japanese normally puts the main verb at the end of the sentence.

So the basic order is often:

topic/subject + object + verb

Here:

マイナンバーカード と 在留カード を 使う

Literally, it is something like:

My Number card and residence card + object marker + use

This is completely normal Japanese word order.

Japanese often leaves out the subject when it is understood from context.

So this sentence could mean:

• I use the My Number card and residence card
• Use the My Number card and residence card
• You use the My Number card and residence card

The exact subject depends on the situation. Omitting the subject is very common in Japanese.

使う is the plain dictionary form of the verb, meaning to use or use.

It is the casual/plain form, not the polite form.

Compare:

• 使う = plain
• 使います = polite

In learning materials, the dictionary form is often used because it is the base form you look up in a dictionary.

Yes. マイナンバーカードと在留カードを使います。 is a polite version and is very natural.

The difference is mainly politeness:

• 使う = plain/casual
• 使います = polite

If this is a standalone example sentence in a textbook, the plain form is often used to show the basic grammar pattern.

Because both nouns are being used together as the object of the verb.

Japanese often builds a noun phrase first, then marks the whole phrase with a particle.

So:

マイナンバーカード と 在留カード = one combined noun phrase
を = marks that whole phrase as the object
使う = use

That is why both card names come before を.

マイナンバーカード is a modern borrowed-style term, so it is written in katakana.

在留カード contains:

• 在留 in kanji, which is a Sino-Japanese word meaning something like residence/stay
• カード in katakana, because card is a loanword

This mix is very common in Japanese. Many everyday words combine kanji and katakana.

No. Normal Japanese is usually written without spaces.

So this would normally appear as:

マイナンバーカードと在留カードを使う。

Spaces are often added in beginner materials to make the sentence easier to read and to show where words or particles are.

Yes, it can be a complete sentence in Japanese, especially in context.

Japanese often allows short, context-dependent sentences. Even without an explicit subject, マイナンバーカードと在留カードを使う。 is grammatically complete enough to stand on its own.

That said, in real life it might also appear as part of a larger explanation, such as instructions or a description of a procedure.

Not if you want to say exactly these two items and no others.

と gives a complete list:

• A と B = A and B

や gives a non-exhaustive list:

• A や B = A, B, and things like that

So:

マイナンバーカードと在留カードを使う
means you use those two specific cards.

If you said マイナンバーカードや在留カードを使う, it would sound more like use things like a My Number card or a residence card, which is a different nuance.