This is the problem with the internet in general. People putting on things that are wrong. Not checked. Derek's labeled switch does not even match the diagram he shows.
As far as that two position ignition switch. You can't get it wrong. It makes no difference which wire goes to which terminal.
Use Phil's switch hook up. He knows what he is doing.
As far as your questions:
1. You now know why headlights come on at first click. You have park and headlights wiring swapped. As Kent has noted and Phil has pictured and your diagram shows.
2. The non blinking is because the tail lights are not connected.
3. The tail lights not connected and the ground for gas gauge are not causing dead battery.
4. The knob on the headlight switch is not designed to smack into the dash. So a clearance is normal if you have the shaft installed properly.
5. If you have a new switch, it is probably good. They don't fail often.
6. Your battery going dead could be anything. Probably something you wired wrong....or a bad battery. Go out after dark and observe any light on somewhere. Be sure key is off. Be sure ammeter is wired properly. It sounds like everything electrical is new. Installed and wired by you. Is that right? Do you have a glove box light or a under hood light? Newer radio? Bluetooth? HERE
] is how you check to see if you have a draw on the battery with everything off.
The labeled headlight switch used by Derek is from Deve's website....and it is wrong. It is unfortunately splashed all over the internet including the HAMB. I don't know if DEVE made the picture or he copied it from somewhere.ALWAYS USE THE SHOP MANUAL.