Connect 9 V battery to Arduino Mega 2560 directly?
Yes. On this page, you can see that you can safely connect 7-12V to the VIN pin.

Furthermore, you can simultaneously connect the USB; your Arduino will automatically draw power from the appropriate source.

Note that the power supply jack pin is connected to the Vin pin through a diode. Do not connect a battery and an external power supply, since a sufficiently high power supply voltage will try to charge your battery, which may be bad news for the battery.