If it is 5 ml per 50 gallon, then it's 0.5ml for 5 gal. I usually use about 2-3 drops per gallon in mine. For a 5 gallon unfiltered tank, ideally you should do 50% mid week and 100% end of week just to keep his water free of unwanted chemicals.
Yes, new fish usually take up to 2 weeks to get use to their new homes, depending on the condition they were in before and their current set up. I was lucky that all mine pretty much adjusted quickly like a fish to water (no pun intended :-D) so they saved me from the worries.
Good luck with yours. Just keep the water super clean and observe for any changes for now. If he is eating, then he is probably not feeling so bad. I think he is going to color up nicely
ETA: really my senile moment! lol I forgot to add that as for the lights, they have the same sleep cycle as us. So during the day, they would prefer some light, and at night, you need to turn off the light so they can sleep. But good thinking to keep the light off for the first couple of days to let him relax a bit. After that, he should be following your sleep cycle too.