will distance running (.5 miles and above) benefit my sprinting and hurdling (100, 110h, 300h)
No it will not. Read posts on this site about acceleration work, max velocity speed work, speed endurance and special endurance. Also read about intensive and extensive tempo. Weight training is also important.
A lot of people warm-up with mile jogs. I would not go over that as there is absolutely no benefit other than maybe a very long warm-up (better for those in cold places).
I don't think that a mile jog is ever the best warmup option regardless of temperature and as stated above I'd avoid too much distance running if you want to max out your potential as a sprinter.
I wonder if people have ever heard of the search function…
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