secondary fuse box

1. No, it's not for when you are using a relay, can be applied at all times.  If you were to add up the current draw by each bulb, the total would be somewhat less than the fuse value.  Only way I know of determining how much current a switch is rated for is by it's specifications,  you may be able to open it up and measure contact diameter, spring tensions etc.  Beyond my expertise though.

2.  Yes, an ammeter in series will give you the current.

3.  Either use a clamp-on meter or probe...or a current shunt and millivolt setting on your meter

4.  Depending upon the length of the run, and acceptable voltage drop across the run would determine gauge size.  Doesn't hurt to run oversize wiring.