Will this battery fit my Nemo Special Ops drill?

Yes, if your tool is part of the Special Ops line. It uses the same connection as the pack that ships with those drills and drivers. It will not fit other brands or Nemo's other tool families.

How much longer does it run than the standard pack?

At 6 Ah it holds roughly twice the charge of the smaller Nemo pack, so expect close to double the runtime under the same load. Heavy drilling and mixing drain it faster than light driving.

Does it need a different charger?

No. It charges on the Nemo charger supplied with the Special Ops tools. A full charge takes longer than the smaller pack because of the higher capacity.

Is it worth buying a spare instead of the smaller pack?

Buy the 6 Ah pack if you work long stretches without power or run the drill hard. If you mostly do short jobs, the lighter standard pack keeps the tool better balanced.

The battery pack only. The charger and carrying case are not included unless you buy them with a tool kit.

Can I leave it in the case between jobs?

Yes, but store it partly charged rather than fully drained or full, and keep it out of extreme heat. That is standard care for lithium-ion tool packs.