There was a lot more than "literally nothing" left over after the bomb. But the places were in shambles. It took a lot of work to rebuild, just as it did all of the other +67 Japanese cities that were destroyed from strategic bombing during the war. There was little radiation on the ground because the bombs were detonated at high altitudes.

There was a big thread on this here a little over a week ago.

Here is the thread from 10 days ago

To address your specific questions:

As /u/restricteddata pointed out, there was a lot more than "nothing" left after the bombs. In both cases, the bombs created intense areas of destruction that left the rest of the city intact around the blast zones. In Nagasaki, the topography of the city limited the bulk of the damage to a single valley. Most of Hiroshima's productive centers were gone, but the main train station and the outlying portions of the city were still there. Even in the damaged areas, ground level and underground infrastructure survived. Sewers and water mains were often cracked, but they were repairable. Roads were still there. Street car tracks were still there.

There wasn't much actual radiation leftover in either city. Both bombs were airbursts, which tend to maximize the force of the blast while sending the bulk of the fallout up into the atmosphere. Immediate radiation concerns were not nearly as strong as you'd imagine, looking back from the present day. This is mostly because regular people didn't really understand the threat of radiation yet, and much of what we know about it now came from studying the atomic bomb victims.

In later years, once radiation had gotten its reputation, people didn't really get over the stigma of having been exposed. For example, it was difficult for atomic bomb survivors to get married because other people feared the possibility of genetic defects. Dealing with the discrimination directed against atomic bomb survivors continues to be one of the main goals of the atomic bomb victim's movement.