If someone is being led to his death by bes din (a Jewish court), is he supposed to try to escape, since, in general, saving one's own life is paramount? More: normally, we say that if someone is out to kill another, the latter can kill him to defend himself. Does that apply here: is the doomed man allowed, if necessary to save himself, to kill the employees of bes din who are leading him to his death?
About your second question, defending himself by killing his executioners: Mishneh Lemelech (Hil. Rotze'ach Ushemiras Nefesh 1:15) implies that no. He says that in cases where extrajudicial killing is permitted (e.g., a goel hadam pursuing a murderer, or a zealot attempting to kill a Jew consorting with a gentile woman), then the intended victim may indeed protect himself by killing the assailant; but not where the killing is a mitzvah, as would be true of a person convicted of a capital crime.
Not sure about escaping, although perhaps we can prove that, at the very least, it's not a mitzvah and may indeed be a sin. In the story of Shimon ben Shatach's son who was convicted based on false testimony (Rashi to Sanhedrin 44b ד"ה דבעיא, and Yerushalmi Sanhedrin 6:3), we see that he willingly went to his death without making any attempt to flee.
Agreed that a person found guilty should accept their sentence; here's a different source.
There are several different Midrashic explanations to Deuteronomy 25:11-12, involving a woman trying to save her husband. Several say the phrase to save her husband from his fellow excludes either saving him from an agent of the courts (carrying out the death penalty), or the wife of a court agent (saving her husband, who was acting lawfully, from an assailant). (In Hebrew -- prat l'shliach beit din, or prat l'eishet shliach beit din.) Depending on how you read that, I think you would also conclude as Alex did.
Regarding the first question, if the convicted should attempt to run, there are two cases - first if the convicted is guilty, and second if the convicted knows himself to be innocent.
The Minchas Elazar in a teshuva (1:18) writes that if the convicted is guilty, then he has a responsibility to allow the judgement to be carried out, as this is his only way to attain atonement. If the convicted is innocent, Minchas Elazar is less sure. He suggests the proof from the son of Shimon Ben Shetach referenced in Alex's answer, however he rejects it as inconclusive, as it may have been that he was well-guarded and unable to run away even had he wished to. He leaves the question unanswered.
In a later teshuva (1:73), he responds to several suggested arguments both for and against running away.
Point 1 - He should run away -- The convicted has the ability to overturn the judgement even after it has been decided by bringing new evidence. [M.E. - That only shows that he has the ability to alter the verdict, not to subvert it.]
Point 2 - He should not run away -- This one is a bit too technical and complex to summarize. [M.E. - The response is equally difficult to summarize.]
Point 3 - He should not run away -- The commandment of לא תסור, to follow the instructions of Beis Din, applies even when you know they are making a mistake, as the Chinuch writes. [M.E. - True, but לא תסור is not one of the commandments for which one must give up his life. Therefore, one would violate the commandment of לא תסור and run away to save himself.]
Point 4 - He could run away -- The Shevus Yaakov (2:106) writes that someone who is in a situation in which he has a mitzvah to give up his life על קידוש השם can run away, but it is middas chassidus to not run away. The same would apply here. [M.E. - The Kessef Mishna contradicts this opinion of the Shevus Yaakov. (Minchas Elazar then goes on at some length to analyze the opinion of the Kessef Mishnah)].