I haven't added the corydoras yet (still waiting for lfs to get more), but everyone gets along great so far. I do about a 4 gal change once a week. Nitrates are at about 10 ppm when tested right before a water change, and drop to somewhere between 5 and 10 afterward. Keep in mind I have live plants.
Did you change your mind on the neon tetras? A 10 gal is small - if you want neons I would skip the platies to give the neons more space. If you're not adding any neons, I would suggest at least adding 1 more platy so you can have 1 male and 2 females. Having only 1 female - it might get tired of being chased around by the male. Also, you could probably add another panda cory (5 total), they like company.