Shouldn’t it be “affect change” rather than “effect change”?
No. Effect change is correct. Something can “affect your life”, but “you effect something”. Effect means to make something possible. Affect means something is influencing you.
No. The "exception" in which effect is a verb rather than a noun is when it is used in the transitive form meaning "to cause or bring about". So you could talk about how a particular policy might affect the economy, or whether or not human activities and carbon emissions affect the global climate, but if you are talking about causing or brining about a specific condition you would talk about trying to "effect a change".
In simpler terms, "affect" means "to have an impact or influence on" while "effect" (as a verb) means "to cause or bring about".