Εκείνος είπε ότι θα έρθει μετά τη δουλειά.

Yes, Greek could leave it out.

Greek is a pro-drop language, so the verb ending often already tells you who the subject is.
So Είπε ότι θα έρθει μετά τη δουλειά already means He said that he would come after work.

Adding Εκείνος makes the subject more explicit and often adds:

• emphasis
• contrast
• a sense of that person / he in particular

So:

• Είπε ότι θα έρθει μετά τη δουλειά. = neutral He said he’d come after work.
• Εκείνος είπε ότι θα έρθει μετά τη δουλειά. = He said he’d come after work / That guy said he’d come after work.

Είπε is the 3rd person singular aorist of λέω (to say / tell).

So it means:

• he said
• she said
• it said (depending on context, though usually a person)

The aorist is the normal tense for a single completed action in the past.

Compare:

• είπε = said
• έλεγε = was saying / used to say

So in this sentence, είπε presents the act of speaking as one complete event.

Here ότι means that and introduces a reported clause:

• είπε ότι... = said that...

It is very common and completely natural.

In everyday Greek, ότι is often omitted, especially in speech:

• Εκείνος είπε θα έρθει μετά τη δουλειά.

That still sounds natural in many contexts.

You may also see πως used in the same way:

• Εκείνος είπε πως θα έρθει μετά τη δουλειά.

So for reported speech:

• ότι = common
• πως = also common
• omission = often possible in speech

No. They are different words.

• ότι = that
• ό,τι = whatever / anything that

In your sentence, it is ότι because it introduces what he said:

• Εκείνος είπε ότι θα έρθει... = He said that he would come...

If it were ό,τι, the meaning would be completely different.

This is a very common spelling point for learners, because the words sound the same in modern pronunciation.

Θα έρθει is the normal way to say he/she will come.

In Modern Greek, the simple future is usually formed with:

• θα
  • a verb form

Here:

• θα = future marker
• έρθει = the form used after θα

The verb is έρχομαι (to come), and its future/aorist system is irregular, so the form does not look exactly like the present.

Useful comparison:

• έρχεται = he is coming / he comes
• θα έρθει = he will come

So Greek does not say:

• θα έρχεται for the basic meaning will come

Because θα έρχεται usually means something more like:

• he will be coming
• he would be coming regularly depending on context.

This is a very common question for English speakers.

Greek does not follow English-style sequence of tenses in the same way. After a past reporting verb like είπε, Greek often keeps the future marker θα if the action was future from that past point of view.

So:

• Είπε ότι θα έρθει.

can correspond to English:

• He said that he would come.
• sometimes also He said that he will come.

The exact English choice depends on context and style, but the Greek structure is perfectly normal.

So even though είπε is past, θα έρθει stays future relative to what he said.

Greek often uses the article where English does not.

So:

• μετά τη δουλειά literally looks like after the work
• but idiomatically it means after work

That is the natural Greek phrasing.

A few grammar points:

• μετά here means after
• δουλειά is feminine singular
• the article τη(ν) is in the accusative, because μετά takes the accusative in Modern Greek

So:

• η δουλειά = the work / the job (nominative)
• τη(ν) δουλειά = accusative form after a preposition like μετά

Also, τη is just the short form of την here. In everyday Greek, the final -ν is often dropped, so τη δουλειά is very normal.

Yes, absolutely.

Both of these are natural:

• μετά τη δουλειά
• μετά από τη δουλειά

Both mean after work.

In many everyday contexts, μετά τη δουλειά is the more compact and very common version.
Μετά από τη δουλειά is also widely used and may sound a little more explicit, but there is no big difference in meaning here.

So as a learner, you can safely understand and use both.