Generally it is not Brand specific. If it needs SDHC only for example, it must be SDHC memory but can be any brand. If it is SD or SDHC both can be used. IF it is xD you cannot use SD or SDHC.

There is a little speed difference and of course a physical size difference.
Memory stick is more commonly referred to as being a Sony media. Memory card is more in reference to SD(Secure Disk) and CF (Compact Flash) and others. Flash is pretty much thought of as Flash Drives as in the stick/USB type.

Camcorders and digital cameras are designed to be best at there individual jobs. Pretty much all video camcorders have a Photo button allowing the capturing of still shots but there are usually limited to the video resolution the camcorder is set at at the time.
Digital cameras of the compact kind might have a video function but again limited in screen size, frame rate and record length in addition to no control over zoom and very poor audio.
Some Digital-SLR cameras are now shooting in HD with a little improved sound. This would also give you interchangeable lens, sharper optics and outstanding still photos.
The question to ask yourself is...Is video the primary or is great photos more important. Then decide from there the features you need with the other as secondary.
Battery life on the Camcorder and the Digital-SLR should be pretty high with the compact cameras being very short along with short record lengths.

The Time setting should be in the Menu area of the camera. Look under change Date and Time in the users manual.