ItWe can express richly our emotions and everyday experiences using an onomatopoeia.

"It" is the pronoun for singular non-human objects.

In this case it's more natural to talk about "we" meaning a group of people that includes you.

The sun was shining pika pika (ピカピカ).

In English we normally put spaces around both sides of brackets, unless one side is the sentence end punctuation, then we'll just include the space before the open bracket.

It started to rain shito shito (シトシト).

I walked home fura fura (フラフラ).

The Onomatopoeia

This is a subjective fix. Not everyone will say this needs changing, but to me it sounds more natural.

ItWe can express richly our emotions and everyday experiences more vividly using an onomatopoeia.

Onomatopoeia is always an irregular plural. It might make more sense to say "In Japanese, we express our emotions..." just because onomatopoeia isn't used in English conversation very much at all.

A more natural way to say this that should show your intention more clearly is "Onomatopoeia is a colorful way to express our emotions and every day experiences."

The sun was shining pika pika(ピカピカ).

If you were to say any of these sentences in English, the onomatopoeia would be in a separate sentence. Since this one doesn't have an English version, I'm leaving this sentence as it is.

・Doki Doki…

ドキドキ = "Bump bump!" (When talking about a heart beating.)

Before my presentation, my heart was beating dracing. Doki doki (ドキドキ).

In the context of all your sentences, your use of onomatopoeia still makes sense. But if an English speaker did use onomatopoeia, it would be in a "sentence" on its own. This is because onomatopoeia is usually considered an interjection.

I only changed this to "racing" because it's more natural. Since you're nervous, your heart is beating faster.

・Shito Shito…

シトシト = "Pitter patter"

・Fura Fura…

I don't think an English version of this exists, unfortunately.

It can express richly our emotions and everyday experiences using an onomatopoeia.

Or, more naturally:

Using an onomatopoeia (or onomatopoeic word) can richly express our emotions and everyday experiences.

The sun was shining like pika pika(ピカピカ).

In English, it's common to say "[verb] like '[onomatopoeia]'".

Some examples:
- The bomb exploded like, "kaboom!"
- The car speeded past me like, "whoosh!"
- I fell and hit the floor hard, like "bam!"

Before my presentation, my heart was beating like doki doki (ドキドキ).

It started to rain like shito shito(シトシト).

「シトシト」初めて知りました！

I walked home like fura fura(フラフラ).

The Onomatopoeia

"Onomatopoeia" is an uncountable noun, so you don't need an article (a/the) before it.

ItWe can richly express richly our emotions and everyday experiences using an onomatopoeia.

・Pika Ppika…:

The sun was shining pika pika (ピカピカ).

・Doki Ddoki…:

・Shito Sshito…:

It started to rain shito shito (シトシト).

・Fura Ffura…:

I walked home fura fura (フラフラ).

The Onomatopoeia

Concept can stand by itself, no need for "the".

It can express richly express our emotions and everyday experiences using an onomatopoeia.

such as…:

・Pika Pika… -

The sun was shining pika pika (ピカピカ).

・Doki Doki… -

・Shito Shito… -

It started to rain shito shito (シトシト).

・Fura Fura… -

I walked home fura fura (フラフラ).

It can express richlyBy using onomatopoeia, we can richly express our emotions and everyday experiences using an onomatopoeia.

such as…For example...

The sun was shining pika pikabrightly (ピカピカ).

Before my presentation, my heart was beating doki dokiheavily (ドキドキ).

It started to rain shito shitogently (シトシト).

I walked home fura furaunsteadily (フラフラ).

・Pika Pika…:

A colon can also be used here.

・Doki Doki…:

・Shito Shito…:

・Fura Fura…:

It can express, richly, our emotions and everyday experiences using an onomatopoeia.

We can richly express our emotions and everyday experiences using an onomatopoeia.

such as…