pl1338- I don't know how familiar you are with engines, so if I sound a little pedantic, my apologies!
Yes, there are three, and "glow plug" and "heater plug" mean the same thing. If you look in the photo, you can clearly see the glow plug closest to the front of the tractor, along with the flat metal bus bar connecting all three and the 12V feed wire (black with a yellow tracer on mine) connected to the center plug. These are all connected with the small nuts & lockwashers.
Standard test procedure would be to first check for 12V on the power lead when the glow plugs are (supposed to be) activated. Disconnect the center power lead, and hook that up to one lead of a voltmeter; the other voltmeter lead is connected to a ground somewhere. When the switch is turned to the glow position, you should read full battery voltage on the meter. (Be careful not to short the power lead to ground when the switch is on glow!)
Next step would be to check each plug: remove the metal bus bar, and check each plug with an ohmeter --resistance-- from the top of the plug, where the bus bar connects, to ground. The meter should read a very low resistance (almost a short). If the needle doesn't move at all, chances are the plug is burned out.
My 2310 is an '07 model so it might be different than yours, but according to my wiring diagram, there aren't any fuses or relays in the glow circuit, only the ignition switch. The plugs are activated both during "glow" position as well as "start" position on my ignition switch, but I do not have an indicator light-- wish I did!
Hope this helps. WBB in NH