How to tell if a tire should be replaced?
A tire's job is to (not a complete list):


Stay attached to the rim
Protect the tube from damage
Contain the pressure inside the tube (this is why the pressure rating is on the tire and not the tube)
Provide a good connection to the ground


Tubeless tires also do the job of the tube.

The tube's job is to:


Hold air


In the drawing below you have a "Clincher" tire.


A simple guide on the essentials of wheels, rims, and tyres

You have two different problems.


Your tire is badly oxidized which compromises it's ability to do all four of the things listed above. You need to replace the tire.
Your tube is leaking air. This has nothing to do with the condition of the tire. You need to find the leak and replace or repair the tube.