Ask your Dr if you need to use a back up birth control method like condoms the first month of being on the pill. I'm not sure if you have to do that with every birth control pill but I do know with some you do.
So, you never had anxiety and depression until you got the implant? It's really hard to say how long it will take to get out of your system. Another question for your Dr. I would think it would be pretty fast.
No, taking the pill does not mean this will happen again. If by chance it does there are several other birth control pills to choose from.