A palagonite is a material similar to basalt formed by the action of water on volcanic ash.
A volcanic glass such as tachylite, obsidian or palagonite.
Yes. They are called sub-glacial volcanoes, which develop underneath icecaps. They are made up of flat lava flows atop extensive pillow lavas and palagonite. When the icecap melts, the lavas on the top collapse leaving a flat-topped mountain. Then, the pillow lavas also collapse, giving an angle of 37.5 degrees. These volcanoes are also called table mountains, tuyas or (uncommonly) mobergs. Very good examples of this type of volcano can be seen in Iceland, however, there are also tuyas in British Columbia. The origin of the term comes from Tuya Butte, which is one of the several tuyas in the area of the Tuya River and Tuya Range in northern British Columbia. Tuya Butte was the first such landform analyzed and so its name has entered the geological literature for this kind of volcanic formation. The Tuya Mountains Provincial Park was recently established to protect this unusual landscape, which lies north of Tuya Lake and south of the Jennings River near the boundary with the Yukon Territory. From: http://en.wikipedia.org/wiki/Volcano#Subglacial_volcanoes
The base of a volcano is a part of the earth's crust. It is created due to pressure in the molten magma below the crust finding a weakness in the crust that gives the lava a pathway to the surface.