no start (crank) hot can be cause by heat soak solenoid or the starter , poor connections and heat soaked battery cables can also affect cranking , may be time for a new starter and possibly some heat shielding , factory had a metal solenoid shield attached to the block
certain headers (like atr style) make heat issues on starter and cables worse than the factory setup
as for battery running down quickly , could just be the starter load is higher due to age or contamination or the battery could just be weak old and time for a replacement , have it load tested or just replace it with something with a higher cca and reserve rating