Answer
Yes, Two rays with a common endpoint must be coplanar.
No, Three rays with a common endpoint are not necessarily coplanar.
Work Step by Step
We are going to imagine a tissue box to help visualize the answer to this problem.
First question: Yes. Choose any two edges of the box that are connected by a corner (two rays with a common endpoint) and these two edges (rays) define one side of the box; or one plane.
Second question: No. Choose any three edges of the box that are connected by a corner (three rays with a common endpoint) and you will see that these three edges (rays) define two sides of the box or two separate planes.
