This will be powered by a 3.7v Lipo battery (3.5 - 4.2V). The RAW pin on the schematic can be ignored since the VCC will just be the Lipo battery, and not regulated.
If i just use the internal clock (8MHz), do i just leave pins 7 and 8 open?
If there is no LED attached to pin 17, SCK, do i leave pin 7 open?
I will use the I2C lines. Should i use the pullup resistors? and what resistance should they be?
In terms of programming with Arduino, can i just use the FTDI Basic board (3.3V or 5V) to upload the program or what should i do here?
yes. Any unused IO pins should be set to Input and have their internal pullup resistor enabled so they don't oscillate & consume power.
yes.4.7K to VCC. Maybe lower, depends on your I2C loading. More parts = lower resistor value. 3.3K, 2.7K. 4.7K should be good starting point.
search for a recent forum posting (Thurs, Fri) for installing bootloader into internally clocked device. Requires fuse change to use internal oscillator vs the external crystal board types. Then you can use FTDI Basic or equivalent.
The FTDI power connection connects to VCC on the promini - so if the FTDI is set for 3.3V, the 328 will see 3.3V for its Vcc. And if set to 5V, the 328 will see 5V. 50ma is plenty for programming.
An 8 MHz board will program correctly with either voltage.