As for the missing episodes, here's summary of what has happened, which is available in longer versions elsewhere.
BBC TV series from the 1960's were usually made with the actors' contracts saying that the BBC had the right to show them once as scheduled, then one repeat later on. After that, the BBC weren't allowed to show them again unless they paid the actors for the right to do this, so everything was due to be destroyed eventually. The exception to this was overseas sales. Foreign TV companies often bought the rights to show and repeat BBC series such as Doctor Who as many times as they liked. There was no such thing as syndication in Britain at the time, because there were only 3 TV channels, BBC1, BBC2, and their rival ITV. The BBC didn't foresee the home video market.
There have now been 10 Doctors. Out of these, only episodes by the first 2 Doctors, William Hartnell (first shown 1963-1966) and Patrick Troughton (first shown 1966-1969) are missing, although a few episodes by the 3rd Doctor Jon Pertwee are available only in black and white or not in their original quality. Patrick Troughton has more episodes missing than William Hartnell.
It seems that these episodes were destroyed over a period of only a few years, ending in 1978. From 1978 onwards a campaign has been going on to recover and restore missing episodes. As this is nowhere near completion, it's pretty obvious that it's an impossible task, so the only way to restore these missing episodes is by using computer technology or to actually remake them. As technology has advanced considerably since the 1960's this seems to be quite possible so long as people have enough money and enthusiasm.
