There are several reasons why this may be happening, but they most likely all come down to one answer.
For most .gif format pictures to actually run as animation, they have to be opened with a program that allows them to be played eg: Adobe Fireworks.
Most likely you're trying to view the .gif with a program that does not support it's animation
Yes
Plug & Play devices can be inserted/removed while Computer is running.
yes
You don't.
A computer feature that allows a device or peripheral item to be connected to the computer while the computer is running
while waiting for a computer download.
Bad alternator.
Yes - Windows accepts external hardware while it's running without any problems !
Yes - Windows accepts external hardware while it's running without any problems !
If you have downloaded them from a questionable source, than they could be infected with some type of virus or other mal-ware. I would deffinitly scan with at least one virus scanner. If you downloaded them from a reputable source then they should not harm your computer. They may cause your computer to freeze, or preform oddly while they are running.
Probably not enough memory - try installing more memory.
A warm boot.