the damage is on the "shoulder" of the tomato. Looks like sunscald, which later rotted. Need enough leaves to shade the fruits during hot weather.

Sunscald and a little splitting, perhaps. The black spots are a secondary organism, taking advantage of the damage.

I agree, shade the fruits when it's bright and warm out. If there aren't enough leaves to do it, I know some people have made little paper hats for them, or used real hats (baseball caps), or put bags over them. Be creative.

The lower brown leaves often happen naturally as the plant ages... if it's more than a handful, and there aren't any obvious spots, consider your water and fertilizer levels -- you may be watering too much, or not giving them enough nitrogen.

--Alison