A short somewhere would mean you'd be either burning up wires or continually popping fuses. Now a drain, where the battery continually runs down, could be anything from the alternator not charging due to corroded connectors at the firewall, bad grounds to the voltage regulator, bad alternator, loose belt, or some component staying hot with juice when the key is off, like a radio, clock, trunk light, etc. A factory clock will, given enough time. run a battery down.
Turn signals could be a bad switch in the column, bad flashers, bad grounds from the dash/firewall to the engine, the turn signal lights not properly grounded/bad grounds at the bulb sockets, etc.
If you have the money you can buy all new, but if you want a challenge and can troubleshoot, get a FSM, the wiring diagram, a volt/ohm meter and start testing.
