[bumblebeard]

Not OP but I do some of these things with KeePass as well.

For autofill, KeeFox works well for me on Firefox - there's probably something similar for Chrome. I think KeePass will do autotype if you right-click on an entry but it's not a feature that I really use so I'm not sure.

I store my password DB in my home folder and use syncthing to synchronize it to my other computers and my phone.

I don't know about iOS but I use KeePassDroid on Android and it works pretty well.