Is flying an ultralight in a careless or reckless manner illegal?
Your specific question: Is flying an ultralight in a careless or reckless manner illegal?
(Assuming that the "Ultralight" in question qualifies as an "Ultralight Vehicle" and is therefore subject to 14 CFR Part 103)
14 CFR Part 103.9- Hazardous Operations addresses this for "Ultralight Vehicles:"
(a) No person may operate any ultralight vehicle in a manner that creates a hazard to other persons or property.
(b) No person may allow an object to be dropped from an ultralight vehicle if such action creates a hazard to other persons or property.
So, unlike operations subject to FAA pilot and aircraft certification standards and regulations under 14 CFR Part 91, (specifically 14 CFR Part 91.13), which uses the wording "careless or reckless," 14 CFR Part 103.9 uses the word "hazard," which I believe would be applied in a similar manner by the FAA.
(emphasis is mine)
Doing anything carelessly or recklessly (i.e. in a manner that puts the lives of others at unnecessary risk) is illegal. Flying an ultralight is no exception.
§ 91.13 Careless or reckless operation.
(a) Aircraft operations for the purpose of air navigation. No person may operate an aircraft in a careless or reckless manner so as to endanger the life or property of another.
(b) Aircraft operations other than for the purpose of air navigation. No person may operate an aircraft, other than for the purpose of air navigation, on any part of the surface of an airport used by aircraft for air commerce (including areas used by those aircraft for receiving or discharging persons or cargo), in a careless or reckless manner so as to endanger the life or property of another.
Careless and reckless doesn't mean what many people seem to think it means, so here are the definitions given in Wikipedia. Put simply, if you were being careful enough to ensure you were not doing dumb things near other people, then you are not actually being careless, are you?
Recklessness: willingly taking an initial action that a reasonable person would know will likely lead to the actus reus being committed, e.g. drinking alcohol and then driving as a result of automation due to intoxication.
Carelessness (also known as negligence): failing to exercise due diligence to prevent the actus reus that caused the harm from occurring – rarely used in criminal law, often encountered in regulatory offenses (e.g. careless driving) or in the civil law tort of negligence – these are known as strict liability offenses.
Source for both the above quotes: https://en.wikipedia.org/wiki/Recklessness_(law)