Я сразу понял её намёк и перестал оправдываться.

Понял is past tense, masculine singular, so it implies the speaker is male. A female speaker would say поняла.

It is also the perfective past of понять, so it means understood / came to understand as a completed moment.
Понимал would be imperfective and would suggest an ongoing or repeated state, not that sudden moment of understanding.

Сразу means immediately, right away, or at once.

Yes, it can move. Russian word order is flexible. For example:

• Я сразу понял её намёк.
• Я понял её намёк сразу.

Both are natural. Putting сразу earlier gives a slightly stronger feeling of immediacy.

Намёк is the direct object of понял, so it is in the accusative case.

But намёк is a masculine inanimate noun, and in Russian, masculine inanimate nouns often have the same form in the nominative and accusative singular:

• nominative: намёк
• accusative: намёк

So the form does not change here.
Намёка is a different case form, usually genitive.

Here её means her in the possessive sense: her hint.

Compare:

• Я вижу её. = I see her.
• Я понял её намёк. = I understood her hint.

In the first sentence, её is a pronoun meaning her.
In the second, it functions like a possessive word meaning her.

The letter ё represents the sound yo.

So:

• её is pronounced roughly ye-YO
• намёк has -myok in the stressed syllable

In real Russian texts, ё is often written as е, so you may see:

• ее
• намек

But the correct pronunciation is still её and намёк.

Перестал is the past tense of перестать, meaning to stop.

Like понял, it is masculine singular, so it matches a male speaker.
A female speaker would say перестала.

This verb is also perfective, which fits the idea of a completed change: at some point, the speaker stopped making excuses.

Because Russian commonly uses this pattern:

перестать + infinitive = to stop doing something

So:

• перестал оправдываться = stopped making excuses / stopped justifying himself

This is a very common structure in Russian.

The ending -ся makes the verb reflexive.

• оправдывать = to justify someone/something
• оправдываться = to justify oneself, to defend oneself, to make excuses

Here the speaker is talking about his own behavior, so the reflexive form оправдываться is the right one.

After перестать, Russian usually uses the imperfective infinitive, because the meaning is stopping an ongoing or repeated activity.

So:

• перестал оправдываться = stopped making excuses

The perfective оправдаться usually means something more like to manage to justify oneself successfully or to clear oneself once, so it does not fit as naturally here.

Because и connects two verbs that share the same subject:

• Я сразу понял её намёк
• (я) перестал оправдываться

This is one sentence with one subject and two coordinated actions, so no comma is needed before и.

Because the subject is the same for both verbs, and Russian does not need to repeat it.

So the sentence is understood as:

• Я сразу понял её намёк
• Я перестал оправдываться

Repeating я would usually sound unnecessary here.

Yes. Russian word order is fairly flexible, so you could also say things like:

• Я понял её намёк сразу и перестал оправдываться.
• Её намёк я сразу понял и перестал оправдываться.

The basic meaning stays the same, but the emphasis shifts. The original sentence sounds natural and neutral.