Some shooting tips with the C100:
C100 has a native ISO of 850, that means shoot all footage at 850. Stop down or use Polarizer and ND combos to control exposure for exteriors.
Shoot at a 4-5.6 to optimize the sharpness of the lens. Possibly even an 8 for a cheap stock lens. This really depends on the quality of the lens, as some lens that may have a 1.8 setting can start to look pretty soft wide open. Use a longer lens at a higher stop if you are not getting the depth of field look you are going for.
Quality of light matters. The fluorescents in the gym are not created equal to a “Kino Flo” tube. Consider changing the lights you are shooting under. Use unified, single point light sources for sharper details. Turn off or unscrew fluorescent tube in overheads that are not the same color temp. Stay away from shooting interior shots under warehouse mercury vapor lights. Steer clear of ebay cheap LED panels, and rent high quality light sources if you need to. Choose locations that are naturally lit already like outside, use a window for side lighting subject. Shooting against the shade side of things, this allows for sun lit backlighting, but background is shaded so it does not overexpose. Shoot the C100 like film, so use an incident meter to set exposure and judge backlight overexposure. Manage backlight exposures and keep inside of +3 stops.
For your main interview shot, turning off the overheads immediately over the subject and using 1-2 Kinos on a stands would give you a better look. Leave the background lights on for depth. Light for the old Light, Dark, Light.
Getting something like a Blackmagic Hyperdeck shuttle or Video assist and recording to ProRes or DNxHD 422 would allow for better colors and color correction. Then edit, and render in 32-bit Video Levels to an XAVC-I HD profile. Let YouTube throw away the information it does not need. There is no effective upload size limit on YouTube anymore.
Learn to shoot a color chart before each setup. This will allow for eye dropper color correction of light sources inside Vegas.
Color Correct out the greenish cast from Fluorescent lights in existing footage.
Sony Sharpen lightly can help (<=.250)
Color Saturation levels can help a little, but most of the time your light source is what is producing poor color levels.
Try using Transparent to Black color gradients to add some contrast to the lighting in those flat gyms. This will help direct the eye towards the key subject.
Play with Sony Soft Contrast FX that can add vignette, smooth out skin tones, and add contrast.
Conversely Hit Films Bleach Bypass can create something different to the softcon filter.
Consider dropping color for B&W, and using either of the 2 filters above. This will make the purple issue on your interview subject not so noticeable. B&W can solve a ton of issues with bad interior light sources. Sony B&W + Sony Color Corrector ,in that order, and you can add some color to the B&W tones.