To avoid something, like a dangerous or undesirable situation, is to keep clear of it or to prevent it from happening. The verb evade is a bit more cunning. To evade something is to get around it or to get out of it, usually by a degree of trickery or cleverness. This verb is most commonly used to talk about getting out of paying taxes, getting around legal consequences, or getting out of answering a question directly. This term’s earliest uses in English had to do with escaping literal pursuit or attack; while this specific sense has waned, the notion of escaping something undesirable remains a useful differentiator.
The noun purview is used to refer to the range of operation, authority, or control of something or of someone in a particular function. Purview is most commonly used in locating responsibility or oversight for specified activities or projects. For example, in the U.S. government, disaster readiness falls under the purview of the Department of Homeland Security. You may also encounter this term used in reference to a particular range of insight or understanding. The noun scope, though also indicating extent, does not on its own suggest authority or responsibility. An investigation of wide scope is simply one that is far reaching.