Re: turn signals and hazards not working
If you have a test light I would use that to check fuses. Ground the wire and probe the test light access points in the top of your fuses. There are two in each fuse, it should light on both sides of each fuse. Sometimes it's really hard to tell if a fuse blew by looking at it, not usually but it happens.
I don't see how you could pull the relay for that circuit and they work...unless the circuit is shorted somewhere. Try putting another relay in the blinker relay spot and see what happens. Most relays under the hood are the same, even if they don't look at. Just match up the terminals with the other one. They all have the same numbers. 30, 87, 87a, 86, etc.