(1) Talking an average speed of about .1C, so max of about .2C.
(2)You're assuming a Carnot cycle.
(3)To reach the power levels we are talking about you are going to need either direct utilization of fusion/annihilation products as reaction material or a direct conversion cycle (like D-HE3 fusion).
(4)Or power from an outside source. ...
(5)You keep saying that and it is simply not true. I won't try to argue with you again about it; you clearly have a need to believe in it.
On (1) Thanks. So the energy source opperates all the time / duration of the trip. So there will be no problem with keeping warm in a < -250C eneviroment; but there will be a problem with the crew not being cooked by its waste heat. As there will be no lakes, rivers, or evaporative cooling towers, do you have any idea how to avoid cooking the crew?
How far is the nearest star with a habital planet, would you guess? I think the duration of the trip at 0.1C average speed, is measured in centuries, not decades. I agree a max speed limit of 0.2C is wise (or perhaps optimistic) as we want the Glactic Cosmic Rays to be the main source of radiation exposure, not the collisions with the protons (ionized hydrogen atoms) that drift in space to be larger.
(2) Actually I googled for the typical efficiency of a nuclear power plant, but agree that 2/3 of the generated energy being waste heat that must be dumped into space is what known technology would produce.
I have several posts describing a Carnot limited system for use on the moon that can get better than 80% efficiency. I think any "life boat" for humans will be on the moon, not Mars which will be periodicly (ever 780 days) on the other side of the sun, 2+ AU from earth as meeting its energy requirments is much easier on the moon.
At either site, the life boat's occupants will be only women until they raise some males using the cryo-jug of sperm, and more than 95% of their lives will be under ground in volumes that robot digging and construction machines made before they first of the set foot on their new home.
(3) The not yet achievable pair of energy sources you mention, both release their energy traveling in all directions, so there is no thrust directly available from them. Most of that released energy would just slam into the ship, heating it, but if in charged particles, not very intense EM radiation, those not going out the back of the ship could be turned around via a magnetic field, which need not take much power if made by super conducting coils. (They could radiate into the <-250C space to maintain their operating temperature.)
I think mutual annihilation of particles with its anti-particle makes only EM radiation and the "bottle" for the anti-matter is not easy to make and would require energy, so the D-He3 fusion is surely the way to go; but there is no He3 on earth.
Some postulate it is in the solar wind and some now mine-able from the surface layers of the moon; but I have some post explaining that He is used in vacuum leak detectors as it escapes thru smaller holes than anything else. There is thus, zero reason to think it remains for more than a few seconds "trapped" in the surface layer of "moon dust" instead of leaking out into the surrounding vacuum. He3 is mentioned by people desperate to find something on the moon, that is not already available on earth at a tiny fraction of the cost importing from the moon would have. (Very ignorant or dishonest people, IMO, trying to support moon exploitation for material useful on earth.)
(4) There is no "outside" source once out side the solar wind.
(5) No I don't "need to believe it." I just quote the facts, given by NASA mainly. See posts 124 & 127 for a few of them. (Quotes from NASA)
Time for correction of post 127 has expired:
365 sievers, which is a lethal dose, EACH DAY!
Should be in 100 YEARs. (On a trip more than a 100 years long)
If the planet is already inhabited with advanced life forms, they may destroy earth for sending biological trash to their planet.