A 'fast lens' is a lens with an large aperture (small number). f/2.8 is considered fast, dont know if f/4 is.
Essentially a fast lens lets more light in so you can have fast shutter speeds for the same ambient conditions.
Be aware that the lower the f/ the shallower thefocus plane.
Honestly, I have never used Manual mode, too difficult.
"A" Mode (aperture priority) - tou decide on aperture, camera decides on best shutter - use this if you want to control the depth of the focal plane.
"S" Mode (shutter priority) - you decide on shutter, camera decides on best aperture - use this if you want to 'freeze' motion or get a longer exposure for better colour depth.
"P" Mode (Programmed) - you decide on a balanced shutter/aperture setting.
Some cameras have "auto-iso" which adds a further degree of decision for the camera to make.
Manual mode is just too complex for my liking.
Also try using sRGB colour mode for more vivid colours.