Well, a little good news! While I'm no expert, I have at least some of everything you posted and they're all pretty healthy. I might actually be able to help.
I do mean drains at the bottom of the pot, but also that the soil itself lets water through it. Think of sponges that hold different amounts of water when you squeeze them. Your cactus wants sandy soil so it won't hold much water. Your ivy is less picky but probably wants a peatier soil to keep some moisture around the roots.
Let me know species you have and I'll try to keep helping. Bonsai trees are tricky assholes and I have a love-hate relationship with mine.
Friend