To be honest I'm not sure how to explain this one. But I will try.
Alone is an adjective, feelings of loneliness or being isolated from others
"I all alone, I wish my family were by my side"
"Stop it! Just leave me alone! I don't want anyone to talk to me"
On my own, not receiving help or assistance from others
"Dad, look! I've built this all on my own!"
By myself, is very similar to both, the difference between "by myself" & "on my own" is that we use "by myself" when no one is WITH you, for example
"I want to find out about this on my own" <---- no help from others, using your own resources
"I went to the mall by myself" <---- No one came with me
By myself & alone; alone is more emotional, about feelings that the physical companion. You can be with others, but still feel alone.
"Look, I love sitting by myself, that doesn't mean I'm a lonely person"
"I am surrounded by so many people, yet I always feel like I'm alone.
I hope that answered your questions