on its own

[AirbusA321]

Which of these are correct?

Intended meaning: No doctor or medicine was needed.
The disease disappeared...
...spontaneously.
...on its own.
...by itself.
...by oneself.
...without help.
...on one's own.
...all alone.

Intended meaning: No mechanic was needed.
I repaired my car...
...on my own.
...by myself.
...all alone.
...on/by one's lonesome.

 

[Rover_KE]

Which of these are correct?

Intended meaning: No doctor or medicine was needed.
The disease disappeared...
...spontaneously.:tick:
...on its own.:tick:
...by itself.:tick:
...by oneself.:cross:
...without help.:tick:
...on one's own.:cross:
...all alone.:cross:

Intended meaning: No mechanic was needed.
I repaired my car...
...on my own.:tick:
...by myself.:tick:
...all alone.:tick:
...on/by one's lonesome.:cross:

`

 

[AirbusA321]

When can we use "on one's own", "by oneself" and "on/by one's lonesome"?
Maybe in sentences like these?

Repairing a car on one's own is a good way to save money.
Repairing a car by oneself is a good way to save money.
Repairing a car on/by one's lonesome is a good way to save money.