Im a little rusty but if I remember correctly the front turn signals are meant to stay on with the stock signal/bulbs. They are the running lights and they have two filaments in them. If you are using aftermarket turn signals you will leave one of the wires off because they usually lack the running light feature and have only one filament. Also, the stock flasher relays tend to go bad but a generic flasher relay is about $5 at autozone and plugs right in.
As for the headlight I think you just replace the bulb (35w), sounds like one of the filaments in it has broken.