As stated get the sewer line/lines inspected with a camera and if the seller will not fix before closing then demand a discount or cash back at closing to cover the costs and make sure the contractor you hire in that case is authorized through the city to work on or connect to the city sewer system (not all contractors are, in fact some municipalities only have 1 or 2 authorized contractors they allow to touch their lines). The camera of the lines is something you could maybe get the seller to split with you but for the low cost most contractors charge it is not worth even mentioning (the company I worked for doing sewer and drain work and now use for my properties charges $150 for a camera inspection and you get a file either emailed to you or a thumb drive handed to you of the video of the inspection).
As for the water draining away from the property that could be easily fixed as far adding downspout extenders or could be a more in-depth job of removing fill from around the house and adding drainage piping and gravel with new loam and seed/sod. But again if there are already existing drainage pipes around the house and you can find or access them via a clean out you can get them inspected via camera as well and they may just be collapsed or clogged and a simple repair.
I would not let any of it scare you away from doing the deal, just with now known knowledge you may have to renegotiate the terms of the deal to make the numbers work. I would try and call some contractors around your area and get some numbers to run again and then get back to the seller and let them know of the added costs you would incur in purchasing the property and see what kind of deal you can work out so everyone walks away happy and if the numbers you each need to reach to make the deal a win/win are too far apart then is when you decide to walk away, but always do so in a professional manner as if you walk away on good terms there is a chance in a month or so if the seller still has the property he/she gets ahold of you and bends more to your number.