Loose or sagging plastic gutters will not drain properly, and this may cause their contents to overflow. As a temporary measure, hammer in a wooden wedge between each bracket and the gutter to hold each section in place until you can replace it.
Depressurize your home to help detect leaks. On a cool, very windy day, turn off the furnace. Shut all windows and doors. Turn on all fans that blow air outside, such as bathroom fans or stove vents. Then light an incense stick and pass it around the edges of common leak sites. Wherever the smoke is sucked out of or blown into the room, there’s a draft.