"The test today was easy."
優しい is actually a homophone of 易しい (which has a similar, but distinct, meaning to 簡単) and is usually used to describe people. From my experience, 簡単 tends to be used more in common speech (possibly due to the confusion that might arise between 優しい and 易しい, though context would usually make the intent clear). However, 易しい seems to carry the meaning of "easy to understand" whereas 簡単 tends to mean "simple", though both do translate to "easy" and can be interchangeable.
I understand that is necessary, but they should change in Today's test. It means the same semantically, but gramatically in the first sentence (The test today...) "today" is an adverb, in the second (Today's test) "today" is a name. And an adverb is not able to possess something.