He Is Risen

Matthew 28 and Mark 16 add more color to the angel's declaration to Mary and the other women: "He is risen! He is not here":

Matthew 28:5-8  5 But the angel answered and said to the women, “Do not be afraid, for I know that you seek Jesus, who was crucified. 6 He is not here, for He is risen, as He said. Come, see the place where the Lord lay. 7 And go quickly and tell His disciples that He is risen from the dead, and indeed He is going before you into Galilee; there you will see Him. Behold, I have told you.” 8 So they went out quickly from the tomb with fear and great joy, and ran to bring His disciples word.

Mark 16:6-8  6 But he said to them, “Do not be alarmed. You seek Jesus of Nazareth, who was crucified. He is risen! He is not here. See the place where they laid Him. 7 But go, tell His disciples - and Peter - that He is going before you into Galilee; there you will see Him, as He said to you.” 8 So they went out quickly and fled from the tomb, for they trembled and were amazed. And they said nothing to anyone, for they were afraid.

How does Matthew 28:8 reconcile with Mark 16:8?
"They trembled and were amazed" (Mark 16:8) "with fear and great joy" (Matthew 28:8) at what they saw and heard from the angels, and then "ran to bring His disciples word" (Matthew 28:8), saying "nothing to anyone" they met on the way "for they were afraid" (Mark 17:8).

What news had the angels shared with the women about Jesus?
"He is risen!... go, tell His disciples - and Peter - that He is going before you into Galilee; there you will see Him" (Mark 16:6-7).

Who is "she" (John 20:2)?
"Mary Magdalene" (John 20:1).

Does she believe what the angels told her above?
No, she thinks they lied to her and Jesus is still dead: “They have taken away the Lord out of the tomb, and we do not know where they have laid Him” (John 20:2).

Who was "the other disciple" (John 20:3) who outran Peter to the tomb?
John, who wrote this gospel.

Did he go inside the tomb first?
No, he stopped at the door and "did not go in" (John 20:5) until Peter "went into the tomb" (John 20:6).

What is meant by, "he saw and believed" (John 20:8)?
John believed what Mary had said, that the body of Jesus was gone. At this point, they still didn't believe that Jesus had risen from the dead: "for as yet they did not know the Scripture, that He must rise again from the dead" (John 20:9).

What does the detail, "the handkerchief that had been around His head, not lying with the linen cloths, but folded together in a place by itself" (John 20:7) imply?
Jesus rose from the dead, shed "the linen cloths" that had been wrapped around His body, then took off "the handkerchief that had been around His head," folded it and set it down "in a place by itself," and then left the tomb.