How could a radiowave controlled remote-controlled bacterium be possible? Criteria: The receiver for the radiowaves would not be bigger than the bacterium (which is the size of a cyanobacterium) The radiowave signals would control the bacterium's movements and also change dna info on the fly.
This is completely impractical. If you've been inspired by the conspiracy theories about vaccines and 5G, please note that those theories are obvious nonsense to anyone with a little knowledge of both radio and biology.
The basic problems include:
Your receiver and its antenna are too small. At about 2 micrometres, they could pick up radio waves of about 8 micrometres wavelength. Unfortunately, that wavelength is in the infrared part of the spectrum, which means that your bacteria will be unable to receive signals through any significant depth of water, or thickness of animal or plant tissues.
Controlling a bacterium's movement requires having some idea of its orientation. Brownian motion ensures that will be random and rapidly changing.
Changing DNA on the fly depends on if you want to make a specific pre-planned change, or redesign the DNA at will. The pre-planned change could be done via a predesigned enzyme, if you had a way to signal the bacterium to release it. But you don't, or at least, not via radio. Making arbitrary changes requires enough computing power and molecular manipulation to manufacture custom enzymes within the bacterium. You don't have the space or energy supply for that within anything bacteria-sized.
Bacteria communicate via chemical signals. If you include in the same environment special bacteria and capsules that release chemical signals you can control those bacteria.
Trouble is what small capsule could receive a radio wave? You could exploit the fact that microwaves cause some molecules to flip. Some capsules could have an envelope containing molecules that flip on a microwave signal paired with other molecules that don't flip. The envelope could break up releasing the chemical signal.