The exposures are fine, Your exif data shows that,The aperatures vary from f 2.5 to f3.0 and the shutter speeds from 1/500 t0 1/1250. which is no problem.
I think that using manual exposure settings in these lighting conditions may be a little hard for a novice, as you have to be very accurate in these high brightness range conditions, or you burn out the highlights too much.
But as you get more experienced it wold be the way to go.
The main shutter lag problem is finding focus, this takes quite a time on a G series camera. In each of your pictures is a sharp area , but not where you wanted it.
This needs manual focus.
I pre focus on a spot where I know they have to pass and set it with the manual focus .
I then use the view finder and watch some one on to the spot and fire the shutter.
I then look at the review screen and see where they were, when the shutter fired.
The next shot is fired when they reach a spot the same distance before my first chosen spot as the person had been in the review picture.
With any luck they will now be in focus.
The next thing to try is to follow the person in the viewfinder and keep it swinging as you take the shot .This is called panning. this allows you to use a slightly slower shutter speed.
say 1/500 second set at TV
This will allow the f stop to close down more giving you a greater depth of field.
You will not need to be so accurate with the focus, as a bigger area will be sharp.
The view finder is not very accurat on a G series camera, You must reall fill the view finder, then in the actual picture there should still be space all round. It makes a 20% allowance,which is too much .
All this comes with experience, shutter lag was not something one had to worry about with film cameras, as it was minimal. For sports work the new dslr cameras have much shorter lag times, and would be the way to go if this is the type of work you want to specialise in.
But don't get me wrong G cameras are excellent allrounders, and you can learn their foibles and take exceptional pictures with them.
Enjoy your Photography, You have made an excellent start.
Keep asking questions... it helps.
Terry