Electricity: I was wondering, whether we can pass electricity through air over a distance of 100 meters or so as electricity means the flow of electrons and we have seen the discharge or movement of electrons in a cathode ray tube
The cathode ray tube has had the air pumped out. Electrons scatter off oxygen and nitrogen molecules so if you fired an electron beam in air it would be scattered in a short distance. The distance would depend on the beam energy, but it's a lot shorter than 100m. The range of electrons from beta radiation in air is around a metre.
You could argue that lightning is the conduction of electricity through air, though I don't think anyone has ever seriously proposed this as a method for passing electricity through air in domestic applications.
In principle, it is possible, using, e.g., high-current relativistic electron beams - please see, e.g., the review http://arxiv.org/abs/physics/0409157 . @John Rennie offers reasonable arguments, but the very real problems he mentions can be overcome - I don't have time to describe the specific mechanisms (see the review). In experiments, propagation length in the atmosphere of at least 20 m was achieved (30 years ago). Let me emphasize that the relevant research is done mostly for weapons development, not for power transmission, and the results are often classified, so I cannot be sure about the maximum propagation length currently achieved.
Let me also note that it may be easier to use electromagnetic radiation (visible or, say, microwave) for power transmission in the atmosphere. It's for you to decide if this is relevant to your question.
There have been numerous demonstrations by Nikola Tesla, about electricity passing through air. He showed his toy sized boat being operated wirelessly with the current he called Alternating. He showed how he ran a motor with its circuits being wireless. And another example his Tesla Coil.
Nowadays, the HAARP technology in US is trying to implement that, and trying to send electricity through air into the sky to change the weather or other places where it could be consumed. Scientists have tried to send electricity through air to Japan. And i think, if this "flow of electrons can take place in conducting solids and liquids, then why not even in atmosphere?