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[awlright]

Caesar ab urbe effugiebat. Trans mare cum paucis amicis in parva nave navigabat. Piratae
Caesar was escaping from the city. Across the sea, he was sailing with a few friends in the small ship.
quidam, quorum eo tempore multi erant in omnibus maris partibus, eos captos ad parvam
Some pirates, many of whom at that time were in every part of the sea, having been captured
insulam duxerunt ; hic Caesarem captivum tenebant. Pretio viginti talentorum pro vita
they led them to the small island; here Caesar was held captive . With the price of twenty talents having been asked for his life,
sua petito, Caesar risit. Clamavit eos nescire quem cepissent. Promisit se eis quinquaginta
Caesar laughed.. He shouted that he to those that had captured him. He promised himself
talenta daturum esse. Amicos suos Romam misit ad hanc pecuniam quaerendam. Dum
to give 50 talents to them. He sent his Roman friends to look for this money. While they
eos exspectat conabatur piratis imperare ut facerent id quod ipse volebat. Etiam carmina
waited he was trying to order the pirates to do what he wanted himself. Also he had
et orationes quas scripserat recitabat, ac nisi plauserunt, eos stultissiomos appellabat.
recited the songs and speeches which he had written and no one applauded, they were calling him the most stupid.
Cum saepe clamavisset se eos necaturum esse, credebant haec verba inania esse.
When often he himself had shouted that he would kill them , they believed these words to be meaningless

[MiguelM]

You must be careful when using determinate pronouns like "the" in Latin. While sometimes it may be appropriate, "in parva nave" or "ad parvam insulam" are much better translated as "in a small ship" or "to a small island" than "to /the/ small ship" or "to /the/ small island".

Clamavit eos nescire quem cepissent.
He shouted that he to those that had captured him.

That doesn't really make much sense. The relative pronoun often assumes is/ea/id as antecedent. Try this:

Clamavit eos nescire [eum] quem cepissent.

Promisit se eis quinquaginta talenta daturum esse.
He promised himself to give 50 talents to them.

The infinitive future construction demands that the subject be always expressed-- so the "se" would have to be there anyway. You shouldn't, therefore, give it such emphasis. "He promised that he'd give them 50 talents" should do just fine.

"Dum eos exspectabat"
"While they waited"

Eos is accusative, not nominative. So "While they waited for them [his friends]"

Etiam carmina et orationes quas scripserat recitabat, ac nisi plauserunt, eos stultissiomos appellabat.
Also he had recited the songs and speeches which he had written and no one applauded, they were calling him the most stupid.

Close, but not quite. Also note that appellabat is third person singular, so the subject is Caesar. Try this:

Etiam carmina et orationes, quas scripserat, recitabat-- ac nisi plauserunt, eos stultissi[o]mos appellabat.

Good luck!

[Imber Ranae]

Clamavit eos nescire quem cepissent.
He shouted that he to those that had captured him.

That doesn't really make much sense. The relative pronoun often assumes is/ea/id as antecedent. Try this:

Clamavit eos nescire [eum] quem cepissent.

It's an indirect question, not a relative clause. That's why it's subjunctive. "He declared that they knew not whom they had captured."

"Dum eos exspectabat"
"While they waited"

The original "Dum eos exspectat" is correct, but your translation fits English idiom better than translating it as present tense would.

[MiguelM]

I wasn't questioning the subjunctive. "He shouted that he to those that had captured him.", and added [eum] to make the Latin clearer. You're right in that it is indirect interrogative, though, and so perhaps a better clarification would have been "Clamavit eos nescire [quid is sit] quem cepissent"

I assumed all the Latin was correct, as he was trying to translate it. I listed it also for convenience's sake. The point is that 'eos' refers to amici and is not a nominative. Thus

"Amicos suos Romam misit. Dum eos [amicos] exspectat"
"He sent his Roman friends. While they waited" should rather "He sent his Roman friends. While he waits for them"

[Swth\r]

Caesar ab urbe effugiebat. Trans mare cum paucis amicis in parva nave navigabat. Piratae
Caesar was escaping from the city. Across the sea, he was sailing with a few friends in the small ship.
quidam, quorum eo tempore multi erant in omnibus maris partibus, eos captos ad parvam
Some pirates, many of whom at that time were in every part of the sea, having been captured
insulam duxerunt ; hic Caesarem captivum tenebant. Pretio viginti talentorum pro vita
they led them to the small island; here Caesar was held captive . With the price of twenty talents having been asked for his life,
sua petito, Caesar risit. Clamavit eos nescire quem cepissent. Promisit se eis quinquaginta
Caesar laughed.. He shouted that he to those that had captured him. He promised himself
talenta daturum esse. Amicos suos Romam misit ad hanc pecuniam quaerendam. Dum
to give 50 talents to them. He sent his Roman friends to look for this money. While they
eos exspectat conabatur piratis imperare ut facerent id quod ipse volebat. Etiam carmina
waited he was trying to order the pirates to do what he wanted himself. Also he had
et orationes quas scripserat recitabat, ac nisi plauserunt, eos stultissiomos appellabat.
recited the songs and speeches which he had written and no one applauded, they were calling him the most stupid.
Cum saepe clamavisset se eos necaturum esse, credebant haec verba inania esse.
When often he himself had shouted that he would kill them , they believed these words to be meaningless

1) "Himself" is not needed in either cases.
2) He proclaimed that thet did not know whom they had captured. (clamavit... cepissent)
3) While he was xpecting them (Dum eos expectabat).
4) ...and if they did not clap, he was calling them the most stupid. (...ac nisi...appllabat).

EDIT: Now I saw that most of them are already corrected!

[Swth\r]

"Dum eos exspectabat"
"While they waited"

The original "Dum eos exspectat" is correct, but your translation fits English idiom better than translating it as present tense would.

Of course, that's the rule! Dum + present indicative always, no matter what the tense of the main clause is.