Just following one of your links showed a serious error. It almost seems purposely built into the experiment. They took people with "influenza like symptoms", not people positively diagnosed with the flu, then they judged a lessening of symptoms in 48 hours without marking or mentioning when they were infected. Since the flu takes a week or longer to run it's course, these people, or at least the people who got better, did not have the flu. Worse, the data were self reported. Because of that there's no way to judge the data... but in the full paper, I note that age difference has a stronger relationship to recovery than the trial substance (p=0.01 for young vs p=0.05 for older).
This is frequently a fault with homeopathy research. It's rarely carried out by medically qualified people and almost always relates to subjective outcomes. High quality research shows homeopathy not to work.
I could never have gotten away with the language in that paper, and I was in one of the softer sciences (anthropology). They took the age data, for instance, and instead of just saying it affected outcomes, they said (with zero supporting evidence) that it improved the efficacy of the medicine. That's clear bias, they already assume the "medicine" is efficacious. How could any reviewer miss seeing that?