Good idea for a thread.
To reassure you, the only reason such things make the news is because they are so rare - as with any crime. You mustn't let it deter you from going into teaching.
To answer your questions:
1. Have you ever been falsely accused of anything? No
2. How does the school you work for deal with such? When a colleague of mine was accused, the school was relentless and sacked him. This was in the private sector, however. As he was falsely accused (the charges were dropped by police), he certainly could/should have sued the school for unfair dismissal.
3. What should be done immediately should such arise? If you are accused of anything by a pupil (informally), or have any problem with a pupil, tell your colleagues. Do NOT keep it to yourself. In my colleague's case part of the reason for the shock was because none of us knew anything about it. If you do not keep it a secret then it's far less likely that people will think you have something to hide.
4. If you give a pupil detention and he/she is the only one, what is there to stop them making a false accusation against you? Do teaching assistants stay behind as witnesses? Otherwise its your word against theirs or even two of them if they both hate you that much because you've detained them. This is why most classrooms have (or should have) a small window in the door, so that there is a chance for others to witness your meeting with the pupil. If your classroom does not have this then you leave the door open. If you think there is a real risk of a false accusation for some reason (e.g. you know the pupil has a crush on you) then you invite a colleague to meet them with you if you have something to say to them.
5. As a teacher, do you find this as a great concern in your day to day life? No. As mentioned above, accusations (false or otherwise) are rare. However, as I said in my answer to your fourth question, you are of course mindful of this in your daily interactions with pupils. This not only covers the chance for all conversations with pupils to be heard/witnessed, but also covers treating pupils fairly, not commenting on their appearance or being derogatory towards them, and not having any physical contact with them (and probably other things I've forgotten to mention here).
6. Should classrooms have CCTV to combat such risks? A lot of buses do so what is the risk to maintain order? I work in France, so can't say about the UK, but in France it would be illegal to have CCTV in classrooms. I think CCTV in itself could open up the potential for abuse in extreme cases (e.g. allowing a teacher to prey on vulnerable pupils) and that we have to combat this risk in other ways.
As Mr M says, there are other things to worry about that affect your teaching life far more on a daily basis.