Dried up lava is still called lava. You can't find lava just anywhere. There is lots in California because that state is near a plate tectonic boundary. However, I could go over to the Lake Superior region and see billion year old basalt erupted when the continent was trying to rift apart. If you have a hammer you can break most rocks.
Geologist have special saws with diamond-tipped blades for cutting rocks.
Active volcanoes can go tens of thousands to hundreds of thousands of years between eruptions. However, once magma starts to move up into the volcano it usually erupts in a period of months or a few years. One way to cool off is to take heat from the inside and bring it to the surface. That's what magma does. The biggest volcanic system, the ocean ridges, are under water volcanoes.