2. Is it normal that they show as Icarus?
Yes, you need to pass in -S erupter:all in order to have them detected as a Block Erupter
Must I do it or may I leave them being recognised as Icarus? Does it change anything from practical point of view?
3. BFGminer doesn't show me the temperature, what to do to have it shown?
Block Erupters do not report their temperature.
Ok... I have a radiator and it is a bit warm in the place it touches erupters (not hot) - I hope it's sufficient cooling?
erupter or icarus its only a name at this level. If you have any other devices then you can name them, but then you need -S erupter all -S otherdevice all
A small USB fan for some cooling is helpful.