I got the chess one pretty easily but I'm stuck on "The elements in your password must have atomic numbers that add up to 200". I haven't found a way to satisfy both this and "The roman numerals in your password should multiply to 35" simultaneously. Iodine (I) and Uranium (U) have high atomic numbers which blow out way higher than 200 and I haven't found a way to avoid them.

Edit: OK, just realised that it's case sensitive. So I can use a lower case "u" to avoid it being interpreted as an element.