Verse 1-4: Writer of this gospel Luke was a companion of Paul (Acts 16:10-11; 2 Timothy 4:11; Philemon 1:24, Colossians 4:14).Luke is the only new testament gentile writer. The book of Acts is also written by Luke. Luke addressed his gospel to a man named Theophilus, but it was also written with a wider audience in mind.
Verse 8-10: According to the Law of Moses, incense was offered to God on the golden altar every morning and evening (Exodus 30:7-8, 2 chronicles 29:11)
Verse 15-16: John was great in the sight of the Lord. In Matt 11: 11, Jesus said “those born of women no one has arisen greater than John the Baptist”. John was filled with the Holy Spirit even before his birth (Luke 1 :41)
Verse 17: John was the prophet sent before Jesus (Malachi 4: 5-6) and he was born with the spirit and power of Elijah (Matt 11:14, 17:12)
Verse 21: The crowd outside was waiting to receive blessing from priests (Numbers 6:24-26) and marveled why Zacharia was delayed.