Using what clock?
I thought that 1 Mhz internal was an option - I was wrong . But assume a 1 Mhz crystal.
On an ATtiny85? The hardware can certainly do it, it's how the chips are configured at the factory.
If you're not seeing that option in the IDE then you have an incorrect IDE setup.
1 MHz = less power.
1 MHz = 8 times slower.
I realise that, but imagine two Atmega328: system #1 - 8Mhz divided down to 1 Mhz. System #2 - 1 Mhz crystal, no divisor.
Both systems have a 'final' clock of 1 Mhz. I assume that both would complete a loop of (say) 100 iterations in the same time.
Are there any any notable performance/efficiency differences between system #1 and system #2?
1mHz is 1mHz no matter where it comes from. Performance is the same.
But...the internal oscillators aren't as accurate as an external crystal. They vary a little bit with supply voltage and temperature (see the datasheet). If you need very precise timing you have to use external components (this
is the reason Atmel gives us options).
Also, if I programmed an Arduinos fuses to use the internal oscillator, do I need to remove the crystal to ensure stability?
It won't make any difference to stability because the crystal is completely ignored.
OTOH removing the crystal gives you two extra I/O pins - worth having on a Tiny85!