Fluorescent lamps radiate a lot of ultraviolet.

No. Ultraviolet radiation from standard fluorescent lamps is low and isn’t dangerous. According to results of researches, that were held in USA, the human, spending eight hours of work time by light of fluorescent lamps, gets as much UV-radiation as by being under July sun near Washington D.C. only a little more than one minute. 

Fluorescent lamps are not so safe as incandescent lamps.

Under conditions of proper usage fluorescent lamps can be considered so safe as incandescent lamps.

The main danger for both lamp types connected with possibility to break the lamp. But the quantity of mercury in fluorescent lamps is very small. Luminophors, which are applied in all modern fluorescent lamps, are no toxic. So, it can be affirmed with certainty, that energy saving lamps are so safe as incandescent lamps.

Compact fluorescent lamps create blinking of light when they are working.

Such blinking of light is typical for lamps, which work with electromagnetic start control devices. More modern electronic start control devices work on high frequencies (20-30kHz), in this case there is no blinking. In compact fluorescent lamps (energy saving lamps) are set only electronic start control devices, that’s why there are no optical (blinking) and acoustic (noise) effects.

To use incandescent and fluorescent lamps in common is unhealthy.

Quite the contrary. The discrepancy of radiation frequencies will only increase the frequency light spectrum. But the intensity of fluorescent light is much bigger than light of incandescent lamps, so switching on in addition the incandescent lamps, as a rule, is unreasonable.