Sorry – I’ve been away all day, and haven’t been able to answer.
1.) There are several methods of aligning a mirror so that you can reflect sunlight onto a distant target. This is, as noted above, the basis of the heliograph. During the second world war, the Air Services and the Navy were concerned that people on life rafts would want to be able to signal for help with mirrors. GE included such mirrors in their emergency kits. Two articles by R.S. Hunter in the Journal of the Optical Society of America (Vol. 35, pp. 805+ (1945) and Vol. 36, #2, pp. 110-115 (1946)) told how to use them (After the war was over, unfortunately).
2.)There were several methods described, but the two simplest were those given by 1920s Death Ray and by Chronos. Death Ray’s (appropriate!) is the more obvious, but the method Chronos gives is more elegant, and doesn’t require you to stick out something blocking part of the beam. This method is also described by Albert Claus in Applied Optics Vol. 12, #10, p. A14 (1973) and in Hal Clement’s science fiction novel Cycle of Fire (1957). Arthur C. Clarke describes something similar in his short story “A Slight Case of Sunstroke” from 1958, which is in his collection Tales of Ten Worlds.
3.) I know that Mythbusters tried this and failed, but they really did a bad job of it. They didn’t use people individually adjusting mirrors, but made a big mirror out of small sections (which is actually what Archimedes was said to have done. The idea of using individually controlled mirrors was suggested later by another Greek, Proclus). But his method of adjusting the focus was pretty crude – they never checked them optically, as is evident from the huge size of the “focus”. Ideally, this ought not to have been larger than the reflected spot from a mirror, but it was much larger. (I’m told there was a followup, but have never seen it).
4.) The experimenthasp been carried out successfully, despite the Mythbusters’ failure. In 1973 Ionannis Sakkas of Greece got a team of 60 soldiers to direct sunlight using mirrors onto a ship 160 feet away (in the water) and set it on fire. The result was published (with pictures) in Time magazine, not to menion the London Times and in New Scientist. in 2002 a German team used 500 volunteers to ignite a sail 50 meters away. The Comte de Buffon had performed similar experiments back in tyhe 18th century. See Mlahanas’ website at Archimedes and his Burning Mirrors, Reality or Fantasy?
5.) Archimedes has been adopted as a sort of Patron Saint . of Adaptive Optics (even though, as I say, it was Proclus who used multiple movable mirrors). I’ve seen him cited by at least three works on Adaptive Optics (the engineering technique that uses “rubber mirrors” ) as the father of their discipline.
6.) I don’t really think that either Archimedes or Proclus was able to actually burn ships. I do think it was within their technical capabilities, but I doubt that they ever built the battery of mirrors needed or rehearsed the soldiers in the techniques. There are easier ways to sink a boat.