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In our opinion, gutters should be installed anywhere that the pitch of the roof causes water to shed.
Generally speaking the roofline actually determines where the gutters are supposed to be. Whenever there is water flow coming off the home there should be gutters and it should be all around the home. So, unless your home was designed by Frank Lloyd Wright and it has the proper underground drainage built-in, you should contact your local gathering contractor.
I would rather think your gutter needs a good sealant. If your soffit is sagging, you have some structural issues.Most likely nothing to do with the gutter.
The most important thing would to review its structual integrity. This can be accomplished by removing some of the soffit panels and taking a peak inside. It could be a a rafter tail is comprimised or broken. Therefore, it would need to be fixed by lifting and sistering. (placing dimensional lumber beside the rafter tail and fastening together). Another fix would be to install a column to support the roof. Installing the column would require a stable footing below, (a concrete pad) and lifting the roof to the proper slope and affixing the colum to the sub-fascia board on the eave. The column method would provide the best support over time and combat heavy snow loads, however a "post" would be in the walk path most likely.
Just behind the valve handle there is a "packing nut" that sucures the shut off valve into the body of the unit. Take a cresent wrench and tighten up that nut and this should stop that leak. No need to pay for a plumber.
I think there is a plumbing problem. I would suggest you to take help from plumber. You can call them and they will see if there is any problem. I hire commercial plumbing service NJ experts to solve plumbing problems. You can also look for a plumbing expert in your area and solve this issue.