for problems 1, 2, and 5, it sounds like electrical issues, like you've blown fuses or relays. Double check your fuse box, both of them (in engine compartment and dash) and make sure those havent blown. if you have, see which ones they are and then check connections on that area. did you use both ground wires for the H4H (that is what your headlight bulbs actually are, you need both ground wires as well as the power wires)

for the horns and sidemarkers, why did you cut stuff/solder?? the horns should've used connectors that just plug and played


sounds like its mostly fuses, thats why the headlights are off and the hazards are making noise. I also know that if the battery isnt on right, and you try to start the car with the headlights on, it clicks and wont start – happened to me just the other day. make sure you have a good battery connection.

also (sorry for all the questions): do you have any pics of your setup?? that also might help some things. mostly pics of your connections, etc.