Not having either the flash or the manual in front of me, this is from memory.
1) S3et it to the green dot. That's "Program" mode. High-speed sync is for taking pictures at faster than the X-sSync speed of 1/250 sec., and results in reduced guide number. There is also a switch which controls whether the flash is operating stand-alone, or as a slave to a 550EX or ST-E2, and which channel it's on as a slave. You should set it to stand-alone mode. The power switch has 3 settings, "O" (Off), "|" (On), and the third is Power-saver - it'll power down after so many minutes. This is all explained (if tersely) in the manual, which, I regret to say, Canon doesn't have available on-line. At least, the manual's flash front/back picture will give you the "names" of the switches and page references.
2) Minimum shutter speed depends greatly on your lens. I have to assume, from context, that you're referring to minimum shutter speed using fill-in flash in daylight. The flash burst will be on the order of 1/1000 sec. or faster, so it will freeze whatever it's illuminating. Your basic exposure (for the background) is always dependent on the old 1/focal length (* crop factor) rule of thumb for camera motion. Depending on the subject's motion, exposures anywhere from 1/60 sec. on up should be relatively ghost-free under normal conditions. The faster the subject's moving, the higher the shutter speed you should use to "freeze" it under existing light, as your subject is illuminated by both the flash and the existing light.