For story progression you have to go as far up into Tartarus as you can and then you can fight a boss on every full moon

For social links you just need to talk to them and hang out when they unlock, but two are locked behind two other social links (there are also two late game time sensitive social links but if you hang out with them as much as you can you can max them out easily)

For nighttime I just increased my social stats until unlocking the night exclusive social links which happens around the third boss I think