Regrading under deck to protect footings from water
You need lots of fill dirt. Put about 3-4" or more right underneath the deck. Than add lots of dirt to the area outside the deck. Grade down away from the deck and divert the water toward that area of your yard that almost looks like a ditch. Once you get your grade set, throw out some tall fescue grass seed (or whatever you like) and cover it with straw. Water it every day until the grass gets about an inch high. Keep watering it often until it is about 3" high and then you can begin mowing it.