Hydraulic cement is a proven way to seal cracks if installed properly. It has been used on commercial, industrial and civil (dams) projects for many years.
You must open up the crack/joint in a "dovetail" shape. Clean out the area. It can be moist. Mix according to instructions and force and compact into the joint. The material will expand, locking itself in and bond to the existing concrete.
If you do not get rid of the water around your footings, you can expect some water in your basement periodically. Start with the gutters, downspout extensions and exterior grading. If that does not do it, install the drain tile that should have been put in when the house was built.