Budapest - Kiev - Beijing - Shenzhen - Auckland, and same route to return

You need a visa. Transit without visa is not possible in Shenzhen.

Also, two stops in China would limit you to 24 hours anyway. It's a complete non-starter. You must get a visa in advance or change your flights.

Thank you Rob and Vincent for the reply. I only have the tickets booked till Beijing. I still can book the right ticket from Beijing to Auckland.

If I need to change planes twice in China, but the first arrival and the last departure is within 24 hours, which airports could be OK to choose apart from Beijing (because Beijing is fixed already)?
For example transiting 2 hours in Chengdu and leaving China within 24 hours from my first arrival?
And on the way back from Auckland, first have a 2 hour transit in Chengdu (not leaving the airport, just transiting inside), would I need to arrange anything in those tight 2 hours or will I have to do it when I arrive to Beijing where I intend to leave the airport? Thanks!!

Transit without visa (TWOV) is not possible at Fuzhou (FOC), Huangshan (TXN), Mudanjiang (MDG), Shenzhen (SZX) and Yanji (YNJ). There are also special rules at Urumqi (URC). Apart from these, you should be fine for 24 hours transit. On your return, even if you don't want to leave Chengdu airport, you will still need to clear immigration at your first stop in China before you take the domestic flight.