I will answer those questions about which I have knowledge. I will leave the other questions for others to answer.
You state that you live in the EU. Water quality is highly different throughout the EU. Some countries chlorinate their tap water, others do not, and this is just one example.
Where I live, tap water is so clean that any filter will only adversely effect the water quality, because filters increase the chances of bacterial of fungus growth. So I simply use tap water for all my drinking, cooking and so on.
Tooth past with fluoride is better for the enamel than tooth paste without fluoride. Fluoride has a proven strengthening effect on the enamel. It is not dangerous for the body. Stories about fluoride being dangerous rely on people not knowing about the huge difference between fluoride (harmless) and fluor (extremely toxic).
Apart from the positive effects of fluoride, toothpaste is not necessary. You may as well brush your teeth with nothing. The most important things are toothpicks or similar (for example, interdental brushes) and a toothbrush. And, of course, not brushing your teeth within the first half hour after eating, as the enamel is temporarily weak during that time and brushing would damage the enamel.
Toothpaste with sugar is a big no-no! I really cannot imagine how someone came to the ludicrous idea of washing the mouth with the very substance that causes caries! As far as I know, sugared toothpaste is only sold in the country where everything has to be extremely sweet (as compared to other countries’ standards), being the US. But I haven’t investigated this in other countries throughout the world, so perhaps there are more countries where this nonsense is considered normal.
Onychomycosis is very hard to treat. The Wikipedia page about onychomycosis provides an excellent overview of the situation, to which I cannot add much.
Yoghurt is advised for its health effects. It is almost always a good idea to consume yoghurt at least three days a week, though even three times a day wouldn’t be a bad idea. Of course, there’s no need to add sugar to your yoghurt. If you do add sugar, beware of the calories and of the effects on your enamel.