Your nitrates are high. What were they before your skimmer problems? Is your skimmer producing bubbles? Are the bubbles fine or large insize? How high does the skimmer cup go up the riser tube which is the tube that empties into the skimmer cup.
I could suggest that you take the skimmer apart, checking the pump for blockages, dirt or something trapped on the needle wheel. If this is dirty or has some blockage then you skimmer should be better. If not, check the venturi inlet to your skimmer whihc is where the pipe that takes in into the pump joins the pump could be blocked with salt or something else. A bit of warm water and vinegar should sort this out as well as cleaning it with a toothpick. Also check the silencer part for any dirt build up becasue as it sucks air it sucks dirt from the outside. If this doesnt help then take the whole skimmer boots and all and place it in a basin with hot tap water and any cheap vinegar and let the skimmer run for about thirty minutes to remove any oils that may have built up. Rinse it well adn let use know.
To reduce your nitrates you can go the probiotic route with products like stability or prodibio and vodka. I have zero nitrates and phosphates and I only use carbon with no phosphate remover or purigen