Flyback NE555N driver and mosfet overheat
Despite NE555N datasheet says output (pin 3) voltage is only about 2 volts lower than Vcc, I have only +6.3v on pin 3. Is it a digital multimeter misreading?


A ordinary digital multimeter will average the pulse train on the gate of the FET into what looks like a DC level. 


  The MOSFET used there is IRF3205, but currents beyond 6-7A force it to heat up, and 10A (with 100-110 Watts on secondary) even more (heatsink is ready to boil water)


An NE555 is a poor choice for driving a MOSFET (even logic-level) as it cannot sink and source much current. Put a monolithic MOSFET driver IC between the 555 and the MOSFET and your power dissipation will improve.


  Does MOSFET overheat due to undervoltage on gate (hence not fully opened) or cracked transformer core? Do I need some other enhancements for this circuit?


Get an oscilloscope (even a relatively old one) and probe the switching nodes. It's the only way to really know what's going on in the circuit.