Я моргнул и снова посмотрел на экран.

They are past tense, masculine, singular forms.

In Russian past tense, the verb agrees with the subject in gender and number:

• моргнул, посмотрел = masculine singular
• моргнула, посмотрела = feminine singular
• моргнуло, посмотрело = neuter singular
• моргнули, посмотрели = plural

So this sentence suggests that the speaker is male. If the speaker were female, it would be:

Я моргнула и снова посмотрела на экран.

Yes, Russian often can leave out the subject pronoun, but here Я is very natural.

One important reason is that in the past tense, Russian verbs do not show person clearly the way present-tense verbs do. For example:

• смотрю clearly means I am looking
• but посмотрел only tells you masculine singular past, not specifically I

So Я helps make the subject explicit: I blinked and looked again at the screen.

Without Я, the sentence Моргнул и снова посмотрел на экран is possible in context, especially in narration, but it is less self-contained.

Because this is a simple case of two actions with the same subject joined by и:

• Я моргнул
• (я) снова посмотрел на экран

In Russian, when two coordinated predicates share one subject, you normally do not put a comma before и.

So:

• Я моргнул и снова посмотрел на экран. = correct

Because the verb посмотреть / смотреть normally goes with на when you mean look at something:

• смотреть на экран = to look at the screen
• посмотреть на экран = to take a look at the screen

For an English speaker, this is just a verb-preposition pattern you need to learn together:

• смотреть на кого? на что?

So на экран is in the accusative case, because на with this meaning takes the accusative.

Because посмотрел is perfective, while смотрел is imperfective.

Here the speaker means a single completed action: after blinking, he looked again at the screen once.

• посмотрел = looked / took a look
• смотрел = was looking / looked for some time / used to look

So:

• Я моргнул и снова посмотрел на экран. = I blinked and then looked at the screen again.
• Я моргал и снова смотрел на экран. would sound like repeated or ongoing action, and would not fit as well here.

For the same aspect reason: моргнул is a single blink, while моргал suggests repeated or ongoing blinking.

Compare:

• моргнул = blinked once
• моргал = was blinking / blinked repeatedly

In this sentence, the idea is one quick action followed by another:

1. I blinked
2. I looked at the screen again

So моргнул is the natural choice.

Снова means again.

So снова посмотрел на экран means looked at the screen again.

A close synonym is опять. In many contexts they can both mean again, but снова often sounds a bit more neutral or literary, while опять can sometimes sound more conversational and can sometimes carry an emotional tone like yet again depending on context.

Here:

• снова посмотрел на экран = looked at the screen again

Yes, Russian word order is flexible, and this sentence could be rearranged depending on emphasis.

The given order is very natural:

• Я моргнул и снова посмотрел на экран.

This presents the sequence smoothly: first blinked, then looked again.

Other orders are possible, for example:

• Я моргнул и посмотрел снова на экран.
• Я снова посмотрел на экран после того, как моргнул.

But the original version sounds the most straightforward and idiomatic.

Normally моргнуть means to blink.

If you want to say wink at someone, Russian more often uses expressions like:

• подмигнуть кому-то = to wink at someone

So in this sentence, Я моргнул should be understood as I blinked, not I winked.

Yes, экран is in the accusative singular after на with посмотреть на.

The reason it looks unchanged is that экран is an inanimate masculine noun, and for many such nouns:

• nominative singular = accusative singular

So:

• экран = nominative
• экран = accusative

The form is the same, but the function is different.

Possibly, depending on context, but again is safer than back if you are translating literally.

• снова directly means again
• looked back at the screen in English can imply returning your gaze to the screen after looking away

That may indeed be the situation here, but Russian does not explicitly say away or back. It simply says:

• I blinked and looked at the screen again.

So looked back at the screen can be a natural English translation in context, but grammatically the Russian is just again.