Programming the mcu for 8MHz operation is straightforward. I run all my battery-operated projects at 8MHz to save power, and I program them via ICSP.
The 8MHz internal oscillator is not very accurate. You can calibrate it but it still varies with battery voltage. This is not a problem unless you need accurate timing. If you do, use a 3-terminal ceramic resonator (if 0.5% is accurate enough), then you don't need the 18pF capacitors.
If you are running the mcu from a 3V coin cell, you don't need voltage regulation for the mcu unless you need a stable analog reference.
You can leave out the reset pin pullup resistor, but it will be more sensitive to noise. So keep the wiring to the reset pin as short as possible and not too close to anything that generates noise. Typically you will only have a connection to the ICSP header, so locate the header close to the mcu and you will be OK without the pullup resistor.
If you will be programming the mcu via ICSP then you don' need the DTR cap (or a USB-to-serial converter unless you need it for communication, or a bootloader).
If space is that tight and you don't need so many I/O pins, consider using e.g. attiny85 (8-pin) or attiny84 (14-pin) instead of atmega328p.