Ok, so Vo to 10k potentiometer. MOSI in my construction is for programming, I'm going to use PB1(OC1A) but I read somewhere that I must connect backlight via some transistor and some resistors - but what?
As you know the ATMEGA8 can sink only 10mA. The LED-backlight requires 100mA in some cases.
Connect a small N-channel MosFet (BS170) to the I/O port via a 100Ω resistor and connect the drain to the backlight cathode (-). Connect a current limiting resistor to backlight anode (+) according to display specifications.
MOSI is used for ISP in almost every application. Despite that you can use it during normal operation as a PWM output.
I would not recommend that, the contrast would be a min or a max, so the LCD could be blank or black.
Use a 10K pot from +5V to 0v, wiper to contrast pin on the LCD. Adjust for optimum contrast