Hi, Angela. You can mix up some mortar and push it in the cracks. Try to get it pushed in as much as possible. When you have it all done, take a big sponge with water and you will be able to rinse off any mortar that is still on the surface. Probably, this will not be a permanent repair since there is no firm foundation under your sign/marker. But then again, it's not really going to hurt anything if you have to fill the present or new cracks in a few years.
Painting the brick will add a lot to your problems. It will make future fixes much more difficult and you would have to paint those again too. There is no reason to paint brick. The bricks and mortar in good condition will last a lifetime. If you search this board and others, you will see how many people want to strip the paint off brick and how difficult this is.