Since the the United States gave a warning to citizens living in Hiroshima that they were going to drop an atomic bomb on them. Did the Japanese prepare for a bombing run? Or did they think it was an empty threat or didn't have time to prepare?
No. According to Max Hastings in "Retribution" the message sent from the Twentieth Air Force to Washington immediately following the bombing of Hiroshima was: "No flak or E/A opposition....Enemy air opposition: Nil."
The warning you reference - the Potsdam Declaration, was also very vague as does not reference an atomic/nuclear weapon at all. The specific language you discuss is "prompt and utter destruction." There is no way that the Japanese would have known what Truman and the allies were referring to. As Hastings states, "[The Potsdam Declaration] was a sham ultimatum, however, because it failed plausibly to describe the nature of the vague sanction which it threatened in the event of non-compliance."
Therefore, there is no way that the Japanese could have prepared for this. Furthermore, Japanese air defense at this point of the war was essentially moot for a variety of reasons including allied bombing of Japanese industry and crippling their shipping of raw materials, the shortage of Japanese pilots, and the preparation of Japan for an invasion of their home islands.
The myth of the US warning Hiroshima citizens comes up on this subreddit a lot, and /u/restricteddata wrote a great post explaining how this didn't happen.
It is worth noting that by that August 1945, it was quite common for single B-29s to make reconnaissance or weather runs over Japanese cities — so just seeing a single (or a couple) B-29s was not enough to give any "hint" of what was to come.
The initial target for the second mission was Kokura. The bombing plane ran into heavy smoke/clouds there (it isn't clear which) and couldn't comply with the visual bombing orders, so went to the secondary target (Nagasaki). There are three possible sources of the clouds/smoke given in the historical literature: 1) just weather (not at all impossible given the volatility of the summer weather season in Japan); 2) smoke from a nearby firebombing raid that took place the night before; 3) deliberate smokescreen created by Japanese workers at a nearby power plant, something they apparently did whenever they saw B-29s (a weather plane went over Kokura several hours before the attacking plane did). I have written a short piece about these different explanations here (I do not know which is correct, and it could be a mixture), but the third is pertinent to your query.
At Kokura, because the plane lingered so long (it made three unsuccessful bombing runs), there was some flak sent up from antiaircraft batteries, and the airmen conducting the run did worry about fighters (which did not materialize). This was part of their motivation to switch to the secondary target. There was no flak (or fighters) encountered at Nagasaki; they made one bombing run (probably did not visually see the target, but that's a separate issue), dropped the bomb, got out of there and back to Okinawa, barely making it before their fuel ran out.