It depend by the type and the make.
A small coffee grinder 100-200 watts.
6 watt bulb for mini lamp
none
Projector replacement lamps can be purchased from many websites. These websites include, but are not limited to Projector Central, Projector Lamp Experts and the auction website eBay.
"Watts RMS" is better represented as "Watts average". Since 1000 watts is 1kw you have "1000 watts average" and you can derive "1Kw average". So 1000 watts RMS will consume 1 Kw
Not enough information is provided by the question, however, it is simple enough to determine the wattage required for the projector with a multimeter. Measure the voltage (120V likely in the US) and current with the multimeter. Then multiply them. For example, if you measure 120 volts and 5 amps, then 120V x 5A = 600 watts. Another device you can find on Amazon is the "KILL A WATT" that your can plug the projector into and it will directly measure the watts or volt-amps of the projector. Now it gets a bit more complicated. If the lamp in the projector is a "high intensity discharge" type lamp (mercury vapor, for example), then the UPS you want must be "fast transfer" so the projector (and lamp) doesn't lose power for any appreciable amount of time. The "fast transfer" UPS's are significantly more expensive than the simple backup battery packs that Amazon sells for less than $100. That type will work with a lamp that is an incandescent type. This answer was provided by an electrical engineer who works in the power systems field.
None, the watts come form the electricity supply and the lamp uses them at a rate of 100 an hour when it is turned on.
1230w
Look at the nameplate
The usual criteria is that the larger the envelope size of the lamp the larger the wattage of the lamp. The terminology of "big bulbs" suggests that the lamp could be in the range of 400 watts.
A lamp post produces exactly zero watts, just like my computer produces zero watts. It is a user of electricity, not a producer. The amount of electricity used will depend on the bulb that is used in the lamp post.
If it a mechanical lock none.