kyuuri to tomato wo usuku kitte, sarada wo tukurimasu.

Because きゅうり と トマト works as one combined noun phrase: cucumber and tomato.

So:

• きゅうり と トマト を = cucumber and tomato as the object
• both are being cut

Japanese often puts the particle only once after the whole list, not after each noun.

So this means:

• きゅうりを、トマトを切って is possible in some contexts, but
• きゅうりとトマトを切って is the most natural way here

Here, と means and.

So:

• きゅうり と トマト = cucumber and tomato

This と is used to join nouns in a complete list. It sounds like you are specifically naming the items involved.

Because 薄く is the adverb form of the い-adjective 薄い.

• 薄い = thin
• 薄く = thinly

It modifies the verb 切って:

• 薄く切って = cut thinly / slice thinly

This is a very common pattern:

• 早い → 早く = fast → quickly
• 小さい → 小さく = small → in a small way / made small
• 薄い → 薄く = thin → thinly

It can naturally mean either one in English, depending on context.

In this sentence, the idea is:

• slice the cucumber and tomato thinly
• or cut the cucumber and tomato into thin pieces/slices

Japanese often leaves the exact cutting style a little broader than English does. The important point is that the pieces are thin.

Because the て-form is being used to connect actions.

The sentence has two actions:

1. きゅうりとトマトを薄く切って
2. サラダを作ります

So the structure is basically:

• Cut the cucumber and tomato thinly, and make a salad.

In natural English, this may sound more like:

• Thinly slice the cucumber and tomato and make a salad.
• Slice the cucumber and tomato thinly to make a salad.

The て-form often links actions that happen in sequence.

Because サラダ is the object of a different verb.

There are effectively two verb units here:

• きゅうりとトマトを薄く切って
• サラダを作ります

So:

• を after きゅうりとトマト marks what is being cut
• を after サラダ marks what is being made

Each verb can have its own object.

Because the main action being stated at the end is make a salad.

The sentence is not just describing cutting vegetables. It is describing the overall activity:

• first, cut the cucumber and tomato thinly
• then, make a salad

Japanese usually puts the main verb at the end, and here that main verb is 作ります.

So the sentence emphasizes the completed action/purpose: making a salad.

This is normal in Japanese.

Only the final verb in the sentence usually shows the politeness level clearly. Earlier verbs that are in て-form do not need their own polite ending.

So:

• 切って is just the connective て-form
• 作ります is the final verb, so it carries the polite style

This is very common:

• スーパーに行って、パンを買います。
• 家に帰って、寝ます。

The whole sentence is still polite because the final verb is polite.

Japanese often leaves the subject unstated when it is clear from context.

So this sentence could mean:

• I thinly slice cucumber and tomato and make a salad.
• We thinly slice cucumber and tomato and make a salad.
• Please thinly slice cucumber and tomato and make a salad.
  (though a direct instruction would usually be phrased differently)

By itself, with 作ります, the most natural default reading is something like I make a salad or we make a salad, depending on context.

Because トマト is a loanword, and loanwords are usually written in katakana.

• トマト comes from a foreign-origin word, so katakana is standard
• きゅうり is a native Japanese word, so it is commonly written in hiragana

Technically, きゅうり can also be written with kanji as 胡瓜, but in everyday Japanese it is very often written in hiragana.

To some extent, yes, but the given order is very natural.

The basic structure is:

• [objects + adverb + cut in て-form], [object + make]

So:

• きゅうりとトマトを薄く切って、サラダを作ります。

This sounds smooth and standard.

Japanese word order is more flexible than English, but particles show each word’s role. Even so, learners should treat this sentence as a very natural model and not move things around too freely at first.

It can suggest both, depending on how you translate it.

Literally, it is connecting actions:

• cut thinly, and make a salad

But in natural English, the relationship is often understood as:

• slice the cucumber and tomato thinly to make a salad

So here the first action is not random. It is part of the process of making the salad. The て-form often links actions that are sequential and closely related.