You should expect the dash lights to dim when you pull out the light switch because you are adding the resistance of the headlight circuit (the path through the switch, the wiring, the bulbs and the grounds) to the circuit powering the dash lights. Whether this is problematic depends on the amperage decrease amount caused adding the headlight circuit to the dash light circuit. You can measure this with a multimeter, but given the way your dash lights are illuminated, it appears you are conducting this test without running the engine. There is rarely a need to do this, and while the car is running the alternator will increase the current in the system to account for the increased usage. So before you conclude this is a problem, check to see if you are seeing a pronounced dimming with the car running. If so, then you have a problem in the headlight circuit. If not, you may want to dig deeper into this, or alternatively consider what many of us have done.
If you modify the headlight circuit to incorporate a relay into the circuit, you provide a more direct path for the current that actually causes the headlights to light up. More importantly, you separate this current from the headlight switch, substantially prolonging its life, and from the dash lights eliminating the dimming problem altogether. See here for a good discussion on this:
http://www.danielsternlighting.com/tech/relays/relays.html
Your second problem is probably a ground problem, and it is likely within the taillight assemblies. In short, the current powering the turn signal light is not going directly to ground, but is instead finding a path to ground through the tail light circuit (your dash lights are also in this circuit when you pull out the light switch to position 1). The left side and right side circuits are fused separately, so you may be able to narrow down your problem by observing whether it is worse when signalling to go left v right. If you see this, the taillight assembly on the side causing the dash blinking is likely the cause of your problem. Try grounding the copper strip across the back of the tail light assembly and see if this makes the blinking go away. If it does, add a ground wire to both tail light assemblies.