Visa requirments for Shenzen Airport

Both of your itineraries are definitely eligible for 24 hours visa free transit. Anyway, I would like to inform you that layovers are not the only part that counts for the overall transit duration, but also the flight between the points within mainland China. To clarify, your entire transit time is calculated from your first scheduled landing, in your case in Shenzhen, until your second departure, in your case from Beijing. So, if your entire transit, calculated in the above mentioned method is shorter than 24 hours, you are definitely eligible.

As far as your second layover is concerned, you can definitely apply for 24 hours free entry permit upon landing in Shenzhen. The longer the layover, the chances to be granted a permit increase. Having in mind that your layover is 18 hours long, if you enclose your accommodation booking, booked in advance, you will almost certainly be allowed to exit the airport. Anyway, you should keep in mind that this permit is always issued at discretion of immigration authorities.