The camera goes brings shutter speed down to 1/30 in auto when it believes that there is not enough light, so it sets the shutter speed and aperture appropriate to the conditions. Also the photo will be effected by how much you zoom as this will effect the aperture. So if you have the camera fully zoomed the aperture will have to be higher and the shutter speed has to be lower. Another thing that might make a difference is the way you hold the camera, I am always telling people to hold their camera differently, so that there is less movement and more chance of getting the shot, of course this is effected by the focal length. For DSLRs, the rule of thumb is that you should shoot no slower than the focal length that you are at (converted to 35mm). So if you were shooting at 200mm you would have your shutter speed at 1/200 or faster. This rule can be broken, I break it all the time, but is handy. With bridge camera like yours, the rule is sound, it is just harder to work out the focal length to shutter speed.

Here is the list:
http://support.nikonusa.com/app/answers/detail/a_id/16780/~/approved-sd-cards---coolpix-p100

Yes.
Approved memory cards:
http://support.nikonusa.com/app/answers/detail/a_id/16780/~/approved-sd-cards---coolpix-p100

Yes