I think you will need more than 1650w. Perhaps you could run 2 1650w-110v elements.
Just for reference my 5500w/220v will take 13 gallons of 45 degree water to 170 in 45 Min. in an uninsulated keggle.
The short answer is no. As you said the amount you use will vary depending on the level of carb you want. Bigger beers can more time to carb, due to the alcohol, but you will want a them to age a bit anyway.
Just to add to that point, You want a beer with a higher OG on your cake, so you get some growth &/or you don't have more yeast than you need. If you want to brew a smaller beer you can add some distilled water, swirl & pour off about half the cake...
Leave your beer alone for another week, 2 if you can stand it. Then take another reading. If it is still 022 then you can worry. It will drop closer to your target FG.
The front button or switch turns a quarter turn and you can pull it free from the metal base. Then you slide it thru the hole, click it in the base, then tighten the screws against the back of the panel.