When you said "No" about my medication question I just want to make sure that's "No you don't need authority from the doctor and yes you can take it on"

With regard to the medication, Would it be a good idea to take a copy of my prescription with me because I don't plan on taking the tablets in the box they come in, but rather will have them in pill boxes.
They are very unlikely to notice or care about your medication in any way. It's international journeys where that is much more of an issue. That said, it's a good idea to carry the prescription while travelling in case of some actual medical concern: for example, if you are hospitalised after an accident and someone needs to explain what meds you are on, you lose them and need a refill, things like that. So I'd take it along.