water gettin into basement
Water can enter from under the slab, especially if your home doesn't have a functional sump pump in a sump pit. Water will always find a way in the home if it is the path of least resistance, so step one is to find a way to convince it to go somewhere else. A sump pit and pump will often help, and installing one is a DIY job. Extending your downspouts away from the house will help, as will maintaining sloped grade away from your foundation.
As far as sealing cracks, you really need to epoxy most foundation cracks if you want to really solve the problem. There are very specialized products that you can buy (Simpson brand comes to mind), but it is best left to pros, who can inject the epoxy under pressure the entire depth of the crack.