Will MCP23017-E/SP be compatible with an ATtiny85? ATmega328P?
Yes, they will work.  However, you may need to read over the datasheets to figure out how to talk to them.  Basically, the chip has a set of registers that you can access over the serial interface.  These registers control the pins (direction, level, etc.) as well as provide the input pin state.  To access all 16 pins, you would need to access two 8 bit registers, one for the lower 8 pins and one for the upper 8 pins.