Japanese Grammar

I saw these examples from a book and I would like to find out what is the difference between these two.

1)レストランで野菜を洗ったり、切りたりしています。
2)会社に行くとき、電車の中で本を読んだり、音楽を聴いたりします。

Is this the translation?
1) At the restaurant, the vegetables are being washed and cut. (Stating the present)
2)When I go to the office, I read a book and listen to music while on the train.
Normally is it tari...tarishite iru or tari..tarishimasu?

First, there is an error in the first Japanese sentence.
It’s not 「切りたり」but 「切ったり」.
And your English translation is not right.
The correct translation is "I / we / (he / she) / they) wash(es) and cut(s) …".
When the context is given, the subject of a sentence can be easily understood in Japanese.

But, I’m not sure what the point of your question is.
Anyway, the grammatical elements of these sentences are divided into these components:

1)-tari, -tari
+
2)-suru/ -shimasu
or
-shite iru / -shite imasu

So, you have these combinations of those components:
-tari, -tari suru / -tari, -tari shimasu
-tari, -tari shite iru / -tari, -tari shite imasu

You can understand the rest.

And your English translation is not right.

The translation is perfectly correct.

The correct translation is "I / we / (he / she) / they) wash(es) and cut(s) …".
When the context is given, the subject of a sentence can be easily understood in Japanese.

The point of a translation is to produce a sentence in correct, natural English. It does not matter a whit what can be understood in Japanese.

practically, しています, します have similar meaning.
します　is a polite form of する
しています　is a polite form of している.
if you use ている, it suggests that the action (verb) are continuing or are repeating (every day, every time, or something like..or act as habit).
I (or someone) wash and cut vegetables (everyday).
(sometimes or often) I (or someone) read books or listen musics.

本を読む
I read books.
毎日、本を読む
I read books everyday.
毎日、本を読んでいる
it is my habit that I read books everyday. （毎日　本を読むのが私の習慣です）
時々、本を読む
sometimes I read books.
今、本を読んでいる（ところです）。
I am reading a book right now.
今私が読んでいる本は面白い
the book which I read (am reading) now is interesting.
昨日　私が読んだ本は面白かった
the book which I read yesterday was interesting.

Ah, we interpret the original Japanese sentence in a different way. I think that the context given, the English translation 2) is possible.
And, I’ve never said that the translation as English language is not correct.

Reading the sentence 1), I imagined someone who works washing and cutting vegetables at a restaurant kitchen (as apprentice cook or someone in subordinate work, for example), for the sentence 1) has the same construction as the sentence 2) and the sentence 2) is translated using the subject I. Probably, these two sentences have nothing to do with each other. Anyway, I am not sure which is the meaning of the original sentence,

I agree completely with your theory of translation, but when the interpretation of an original sentence is not correct, its so called translation in correct and perfect English is nothing.