Higher FG Brews

I have a high gravity hefe in the bottle now (OG 1.065, FG 1.019). I gave it 4 weeks in primary (3068 yeast). FG was stuck for about 2 weeks so I just bottled. After 2 weeks it was way too sweet. Waited a week and it's much better now. I'm going to give it another week and I expect it to be great. I realize yeast is consuming the simple sugars and producing CO2 for carbonation but I'm wondering what else the little beasts are doing.

1) If I bottle (and prime) a brew with a higher than it should be FG, can the SG actually drop below FG while conditioning?

2) Does bottle conditioning also restart fermentation?

3) If I were to take a SG reading out of bottle would it be valid or does the carbonation create a false reading?

4) Does higher SG always equate to perceived "sweetness"?

Appreciate any pointers to further study.

Thanks in advance.

It is possible for the yeast to ferment the malt sugars and the additional bottling sugars down below the F.G. reading when you bottled. There are some conditions that may not allow that to happen such as high alcohol content and the temperature that the bottled beer conditions. However, if the yeast does continue to perform, the problem may be that you'll end up with over carbonated beer or worse, bottle bombs.
You can take a gravity reading by pouring the beer into a shallow pan and let the carbonation dissipate. Or if you have a refractometer, take a reading from the bottle and make the calculated adjustments based on your O.G. readings.
Finally, a higher (F.G.?) does not necessarily equate to perceived sweetness. It depends on the style of beer, IBU levels and carbonation levels to name a few of the factors that go into "perceived sweetness".
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