There are those who have reported that the G1 is not the ideal sports camera; I haven't worked with mine enough in sports situations to tell.
If you do have problems, you can always zone focus ahead of time, for instance on a section of ground you expect the action to move through, and wait for the action to come into your "target area." This prefocus method can be done best in manual focus, for if you're in autofocus and you prefocus, then cycle you finger off and back on the trigger button the autofocus will change (it will attempt to reacquire a target,) whereas when the top left focus mode knob is in "MF" you have full control of the lens focus ring, regardless of the shutter button.
One downside of any electronic view camera (LCD or EVF) is the delay time between the event actually happening (e.g. a boy's foot contacting the ball) and you seeing it happen on the screen; by the time you react to the view on the screen, the event in real time may have already passed. The delay time I'm referring to has nothing to do with autofocus, which may or may not have its own, additional, delay time.
One way around this is to use your free eye to view the action optically, timing the shutter release in real-time, after the scene has been composed on the electronic screen. For sports or other action with telephoto focal lengths you have little option, but for wide-angle, close-in shooting, like fast-action street photos, an accessory optical finder on the hotshoe is a real boon.
As for using a manual focus lens on the G1 using adapter rings, you set the camera to Aperture priority, "shoot w/out lens" feature in the menu enabled, and set the aperture manually on the lens; the camera will choose the correct shutter speed automatically. You also have the option of enabling the zoom focus feature in the menu, activated by a two-button push sequence, which magnifies the center portion of the image to assist manual focus.
I haven't yet used legacy lenses manually, but do so on occasion using the 14-45 kit lens. I prefer not to use the zoom focus feature, as manual focus is very easy to distinguish in the EVF itself, and I find the zoom focus assist to be an annoyance that interferes with my composing the scene at the moment of shutter release.
~Joe