I meant Hong Kong, not the airport, but there are a number of ways to get either to the city or the airport. Most simple is bus from SZX to either Kowloon or HKG (airport). Though I wouldn't do it again, you can also take the Shenzhen subway to the border then take the Hong Kong metro on the other side to wherever you want to go. Additionally there is a ferry from somewhere in Shenzhen to the Hong Kong airport, but it's not really convenient from the Shenzhen airport.

If your passport requires a visa for China, then yes you'd need a visa. It does not qualify for TWOV. Also of note, the land border entry to Hong Kong does not count toward the 3 entries one can use to obtain a Hong Kong e-Channel sticker through the frequent visitor scheme.