Jesus

Why didn’t they recognize Jesus when He called out to them?
Jesus was about 100 yards (91 meters) away (1 cubit = 18 inches, which is half of 1 yard, so "two hundred cubits" (John 21:8, see below) = 100 yards).

What else may have kept them from recognizing Jesus?
If Jesus was calling from the eastern shore, the "morning" (John 21:4) sun could have been rising behind Him.

Who shouted, “It is the Lord! (John 21:7)”
The "disciple whom Jesus loved" (John 21:7), which is how John, the writer of this gospel, refers to himself.

How was he able to see Jesus?
He most likely wasn’t.

Then how did he know that it was "the Lord"?
The monster catch of fish most likely reminded him of how Jesus originally had called them to be His disciples: When He had stopped speaking, He said to Simon, "Launch out into the deep and let down your nets for a catch." But Simon answered and said to Him, "Master, we have toiled all night and caught nothing; nevertheless at Your word I will let down the net." And when they had done this, they caught a great number of fish, and their net was breaking. So they signaled to their partners in the other boat to come and help them. And they came and filled both the boats, so that they began to sink. When Simon Peter saw it, he fell down at Jesus’ knees, saying, "Depart from me, for I am a sinful man, O Lord!" For he and all who were with him were astonished at the catch of fish which they had taken; and so also were James and John, the sons of Zebedee, who were partners with Simon. And Jesus said to Simon, "Do not be afraid. From now on you will be catching men" (Luke 5:4-10).

How did Peter react to John's declaration, “It is the Lord!” (John 21:7)?
He left everything - the fish, the boat, the other disciples - behind and plunged into the water to get to Jesus first.

Why did he at least put on his outer garment?
He had been fishing in his undergarment and probably want to stand before Jesus wearing more than just that.

What do John and Peter’s reactions remind you of?
How they reacted when Mary Magdalene brought news that Jesus' body wasn't in the tomb. On both occasions, John was the faster, both to get to the tomb (see He is risen) and to recognize Jesus on the shore. But Peter was the first to step in, both into the empty tomb and into the water to get to Jesus. And for that, Peter has the upper hand: while it's important to recognize Jesus for who He is, recognition isn't enough, for even Satan recognizes Jesus for who He is; for Jesus to be our "Lord," we must step or dive into a relationship with Him.

What is especially commendable about Peter being the one to try to get to Jesus first?
The last time Peter was the focus of Jesus' attention, he had betrayed Him (see Peter denies Jesus). Given how he had failed, one would expect Peter to keep to himself and shy away from even raising his eyes toward Jesus. Instead, he couldn't wait to come before his Lord.

What example does Peter set for us?
When we fail and sin, our pride and Satan will tempt us to hide from God as Adam and Eve hid after sinning. Instead, we must heed Peter's example and come before the Lord, confess our sins to Him, believing "If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness" (1 John 1:9).