A) what is the evidence that this volcano has not erupted recently?

(b) should this be taken as proof that the volcano is extinct and will never erupt again? why or why not?

As explained below.

Explanation:

A volcano is considered to be extinct if it's not erupted in more than 1 million years since the last eruption year.  While some volcano has shown eruptions over 5 lakh years also. There are chances of the eruptions even after this then it's considered to be dominant or a sleeping volcano. The last phase of volcanic eruptions is considered to be taken into account as all of the volcanoes are due to its lava supply form below if cut off the volcanoes cant produce a sufficient amount of ash and molten matter. Volcano showing signs of inflation, abundant degassing of carbon dioxide and sulfur dioxide would well indicate the presence of magma deep below the surface of the rocks. The word dominant in itself a confusing term as any unusual pattern or any sign of unrest in or over the vent of the volcano represents its explosive nature

Bwould be my guess |-/ 

Themes; subfields is the answer