Do I have drainage issues?
You should check a number of things. 


First off have the water in the house checked for high iron content and confer with the neighbors on the same. Red coloring of the curb is likely from high iron content water evaporating and then oxidizing.
The persistent wet spots in the front like this seem to point to the possibility that there is a water main break under the front yard. If this has been going on for some time and was partially under the former driveway it could have led to driveway damage. Best bet is to monitor the water meter at the street hookup and see if there is high water usage going on.
There is always a possibility that there was an underground spring in this area that was covered over when the housing tract was built. Often times there is a possibility as ground preparation for the tract was done there may have been higher level ground scraped away from this area and exposed an latent spring. In either case a year cycle period where there may have been more rain than usual the water table can rise and cause a latent spring to start letting out water. Fixes for this could be complex and expensive in a developed neighborhood. 


You may want to steer clear of this property unless the water source problem is root caused and you understand the potential financial burden of the problem.