The power supply connections are covered numerous times here so if you do a search for power supply wiring you will get the answers you need. :-)
Water flow is is more efficient( like 20% more ) going to the hot end which is the output side as it gives the water time to absorb the heat from the glass.
The flow rate should be supplied by the manufacturer or you could just Google it.
The output side is the negative or Cathode ( best check this but I'm 99% sure) .
Good quality aligator clips are ok for the connection but are relatively big and you will have more chance of getting an electric shock if working near them. I use BP connectors for earth connectors as they have 2 screws. Multiple connector strips would also work, just break off the plastic and use the brass bit. You will find it very difficult to solder to this and if you use too much heat you run the risk of cracking the glass around the post and letting the gas out ( or in, as the tubes are at a negative pressure to atmosphere). You are only using very low amperage, but very high voltage, so you don't need really large and strong connectors as they won't have the tendancy to heat up.
Rich.
I am not completely useless.......I can always serve as a BAD example.