Good learning link.
DIY Solar Panel help - tutorials, calculators and design tools for solar power
Is it normal to run a load while the controller & panel are attached? I know nothing powerfull (like an inverter) should be connected to "load" terminals on the controller itself, but directly to the battery.
You can use energy as it's being made.
Battery acts as a buffer. it pulls the voltage to that of the battery bank 12, 24, 48 volt. The energy producer must be able to supply the needed voltage to charge.
My 12 volt system may receive / need up to 14.1 volts to charge fully / properly.