in this side of Europe
I assume I am from the same "side of Europe", considering the description.
Sadly it is not custom in this side of Europe to announce or plan a visit.
Maybe it is not the custom in the most ordinary situations. But even in this part of Europe, visits in a hospital are limited within certain hours. Just because the patient is at home, it does not mean that the patient needs nothing special.
Moreover, the "visits" in this case are not just any visits, where people end up opening a bottle of alcohol and grilling some pork. And people actually know about the needs of patients.
It is perfectly fine if you tell the people that the visiting hours are XYZ, because the rest of the time is occupied with the treatment and resting. It is OK to do it by phone, by your own initiative.
if one is sick, should simply not come
You cannot make somebody NOT come, once they are at your door.
But you can do what people with babies do: if the person is obviously sick, just tell them that the patient needs the best environment without contaminants, and a sick person will only make things worse. Tell them they are welcome to return once their cold / flu goes away, and in the meanwhile they are also welcome to use the video-conferencing features provided by smartphone apps.
when there are too many people together, or the visit has been going on for too long
If your apartment / house is big enough, take the visitors to another room, and instruct them to keep their voices lower. Remind about the noise whenever needed, to have a comfortable environment.
To initiate this, your parent might want to aid, and use a code-phrase like "I need to rest, please" - so you will know when to move the people out.
It is also in the "spirit" of people in our part of Europe to get offended easily - if you do any of the things above. But it is also in their spirit to forget it rather quickly, so you do not need to worry much.
You placed your decisions wisely - to make the best for your parent, in the current conditions. Please do not feel guilty for hurting the ego of a selfish person - if such person comes to visit your parent.
I define a "selfish person" in this case - the person who makes the visit not for the sake of the patient, but for the sake of going out - similar to going to an amusement park.
I am really sorry for your difficult time, and especially for the troubles of your parent. I hope you can all get through this in the "best" way possible.