1. Incandescent lamps are resistive but don't try using it with low energy CFL lamps unless they are 'dimmable'. The only loads you have to be careful with are things like motors and transformers. You can still sometimes control these but you may need additional components around the triac.
2. I couldn't open your link but my datasheet for the MOC3020 (Fairchild) is probably the same. The resistor can be low wattage (0.5W) as it either isn't conducting when the MOC is off and only has the voltage drop across the triac across it when switched on.
3. Should be OK, I used a very similar one to remotely switch a DVD recorder on. I used PIC --> MOC3020 --> triac --> DVD. I've also used them for switching 1.5H.P. motors without problems.
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