I agree with the other responders; lots of red flags here. But this, particularly, stood out for me:
When his depression gets severe, he sleeps a lot for two or three days. He claims that is not a problem for a significant other.
Sleeping for 2-3 days--not a problem for a significant other--he means YOU. I don't know of any woman who wouldn't have a problem with this. Sure, sleeping it off for 2-3 days is not a problem--FOR HIM.
At least I'll give him credit for being mostly honest (I still believe he may be drinking) about being a lousy partner. I learned a lot of hard lessons when I attempted to live with an alcoholic and one of them is this:
When people tell you who they are BELIEVE THEM. If this guy had more money than Bill Gates, I'd still run in the other direction. No amount of money can make up for the shortcomings he's fessed up to.
I'd thank him for fessing up and then politely exit stage right.