Enginn þeirra kemur í kvöld.

Enginn changes for gender, number, and case.

Here it is:

• nominative because it is the subject
• singular because Icelandic treats none in this construction as grammatically singular
• masculine for a masculine or mixed/unspecified group

Other forms are used in other situations:

• engin for feminine
• ekkert for neuter
• engir if you are directly modifying a plural masculine noun, as in Engir gestir koma = No guests are coming

So enginn þeirra is none of them, not no people with an expressed plural noun.

Þeirra is the genitive plural form of the 3rd-person pronoun they.

After words like enginn, Icelandic often uses a partitive genitive:

• enginn þeirra = none of them
• literally something like none of-them

This is why you do not get þeir here. Þeir is nominative and means they, but the sentence needs the genitive form þeirra.

Because the grammatical subject is enginn, and enginn is singular.

So Icelandic uses:

• enginn ... kemur = none ... comes

Even though the meaning involves a group, the verb agrees with enginn, not with þeirra.

The dictionary form is koma, meaning to come.

Kemur is the 3rd person singular present tense form:

• ég kem
• þú kemur
• hann/hún/það kemur

So here kemur matches the singular subject enginn.

Icelandic often uses the present tense for future meaning when the time is already clear from context.

Because the sentence includes í kvöld (tonight), kemur can naturally mean:

• comes tonight
• is coming tonight
• will come tonight

This is very normal in Icelandic.

Í kvöld is a common time expression meaning tonight / this evening.

It functions as an adverbial phrase telling you when the action happens:

• kemur í kvöld = comes tonight

You should learn it as a fixed everyday expression.

Yes. Enginn af þeim kemur í kvöld is also possible and means the same thing.

The difference is mainly structural:

• enginn þeirra uses the genitive directly
• enginn af þeim uses the preposition af
  • dative

Both are used, but enginn þeirra is a very standard and compact way to say none of them.

No. Enginn already makes the sentence negative.

So:

• Enginn þeirra kemur í kvöld = correct

If you add ekki, you are no longer saying the same thing, and the sentence becomes awkward or changes meaning. For this idea, enginn by itself is enough.