I believe the answers to both questions is... yes!
One way you can improve the function of a small air compressor is to add an air tank, building a greater reservoir of compressed air for you to draw on when you are using an air tool that outstrips the capacity of the compressor.
If you are looking for a tank, try this link :spare compressor tank.
For most DIY type applications it really doesn't matter. Just remember that you need to have a hose or pipe long enough reach from one tank to the other.
Make sure you have access to the drain valves on both tanks to make this convenient for you.
Use the existing coupler on the current air tank. This coupler allows you to plug a connector into it, and once you plug in the connector air will flow into the air line or hose.
You'll need a length of air hose long enough to reach from the coupler of the main tank, to the inlet connector on the second tank. This air hose will have a coupler on one end, and a connector on the other.
Don't plug the connector into the coupler until you have the hose connected at the new tank end.
Into one side of the Tee thread a coupler.
You will push the coupler from your extension air hose onto this connect, effectively connecting the two air tanks.
On the other side of the Tee, consider adding a nipple, an air filter, another nipple, and then another checked coupler.
Just as the connector on your compressor tank has a checked coupling to keep air in the tank when there isn't a connector attached to it, the coupler you've added to the Tee on the new tank will keep the air in both tanks until you're ready to insert an air line connector into it.
And, with the second tank, you have a lot more air to use for your tools, between compressor cycles.
This is important, which is why the secondary tank is installed after the primary. Then air from the both tanks cannot escape back up the supply line from the compressor when the compressor is stopped and the unloader valve open to atmosphere.
Be aware of a little thing called duty cycle. It would be a shame to have your compressor work so hard and so long to fill up the multiple tanks that it burned itself out because you didn't give it a chance to cool off often enough!