Is a cracked brick sign of a deeper problem

Obviously the ideal solution if the birckwork is generally poor is to rebuild the wall.

In this case this doens't seem to be an option. To replace existing ties that have problems or sections of the wall where ties are missing you can get drill and fix wall ties. I believe you can get this type of system from Helifix in the UK but I'm sure similar systems exist around the world. You can get systems that rely on some fairly unattractive face plates but other systems do not rely on this but have a resin bond to the brickwork. You will probably need specialist advice on what the right system for you is and to identify if there are any other issues associated with the poorly constructed wall other than the lack of ties.

You want something with close to the same thermal and moisture properties as the rest of the surround. Best wound be a piece of brick. You could bond it in with thin set since it is not really structural.

If none are handy, you could use pieces of tile layered using thin set to glue it in. Just make sure none of the pieces stick out more than the brick.

You might want to put a skim coat of the set over the whole brick face before tiling to give you a smoother base for a more even finished surface. This ski coat would cover any irregularities with a pieced tile patch.