The legit Hackrf One is known to have frequency smearing, I wouldn’t use one off Aliexpress to transmit without testing it with a spectrum analyzer first (which you probably don’t have if you are buying knockoffs from Aliexpress).
Not exactly, the transmitted power tends to be centered on the frequency you desire, but there are unwanted harmonics off the center frequency. Its like having a fire hose that hits the desired target with water (something on fire), but it also hits everything else around the target in a large radius as well which may be very sensitive to water (precious art, high power transformers, etc)
The blogpost mentions "I guess it's always good to have another SDR just to confirm that we're not polluting other frequencies." and they have an RTLSDR which probably could serve as a good enough spectrum analyzer for this use case?