First of all *not to consider me a conspiracy theorist(, but isn't landing on the moon a questionable issue?
Only to conspiracy theorists. To everyone else, no, it's not a questionable issue. My father in law helped send men to the Moon. I have worked with a number of people who sent men to the Moon. I was once called on the carpet in Gene Kranz's office. I find it extremely insulting to think that it is a questionable issue. So excuse me if my response might seem be a bit insulting.
How would the Gamma rays and cosmic rays affect the equipments on the lunar surface and would these equipments function normally like on earth?
Equipment and humans did not suffer immediate damage given the short period of time that humans did spent on the Moon. One of the effects of mild radiation is increased risk of cancer (but that's a long-term effect). The men who went to the Moon (and they did go to the Moon) did indeed suffer increased cancer rates compared to the Earth-bound population.
Could the enormous amounts of solar energy bursts be avoided somehow for protecting human flesh?
By luck, there were no large solar energy bursts when men were in space on the way to the Moon, on the Moon, or coming back from the Moon. A large coronal mass ejection event did happen on August 7, 1972, but that was (by luck) sandwiched between the Apollo 16 and Apollo 17 lunar missions.
How is it possible for an FM or any kind of data transmission type be achieved in an environment that has nothing but an empty space? How would the electromagnetic waves travel and enter the earth's atmosphere to be captured by the receivers?
This question makes no sense. Look up in the sky during the day. What do you see? You see the Sun. Look up in the sky at night. What do you see? You see the Moon, the planets, stars, and if you live in an area with low humidity and limited light pollution, you even see other galaxies. With your naked eye. The only difference between light and FM is frequency. Both are forms of electromagnetic radiation. Electromagnetic radiation travels unfettered through empty space.
What is the bright lunar surface real temperature and is there a way to equip an astronaut to protect him from the over-heat?
The first defense against the temperature extremes of the space environment is very simple: It's coloration. A spacesuit that was jet black in the visible range but white in the thermal infrared would have quickly killed the NASA astronauts on the Moon due to overheating. On the flip side, a spacesuit that was white in the visible range but jet black in the thermal infrared would have resulted in overcooling. The space suits worn by the NASA astronauts on the Moon were white in the visible range but grayish in the thermal infrared. NASA spent a lot (a whole lot) of money investigating different fabrics, different dyes, and different paints. Passive thermal control is the first step in any space operation against the extremes of space. Active thermal control addresses what little passive thermal control can't address.