Agreed on dropping the MikroE discussion, there's nothing more to be gained from it.
I've checked relevant datasheet, and that code to be working, instead of ANSEL = %00000000 I should use TRISB = %00000000 right?
Not quite. ANSEL is a register which controls if the pins should be used for analog or digital. TRIS is the register controling the "direction" of the pins, when the pins are set to digital thru the ANSEL register... Makes sense?

The 16F628A doesn't have an ADC so there will be no ANSEL register to set but it does have a comparator module which may need to be configured properly, see the CMCON register.

Also, I set oscillator to XT type in fuses config in programmer, to use internal osc.
Nope, if you set it to XT it expects an external x-tal.