It could be worms but where she is laying fairly regular with nice hard eggs I wouldn't think that. As they sap nutrients in the egg making process. Funny thing with chickens one problem could be any of many culprits. Just got to rule them out one by one.
Don't think the two problems are connected necessarily. Runny poo this time of year is semi- normal due the summer heat they consume a lot of water. As far as laying outside and not in a box could be a couple reasons. Another chicken forcing her out of her box,could be a snake in there for...