Well, they are technically correct but none of them sound natural to me.
I would use something like
- There is a way of doing things (prepositional phrase, of being the preposition and "doing things" being the object of the preposition)
- Certain actions have a process
- Each situation has an optimal procedure
- There is a correct way of doing things
- There are ways to do things and that is not one of them....
In the quoted examples:
Everything has it’s own procedure.
Everything has it’s own way.
There is a way to everything.
The 3rd one is probably the best. In the first 2, "everything" is being used as a pronoun. This personalizes "everything" like saying "the mechanic has his own way of doing things", however, "everything" is general and not specific so saying "everything has a way" or "everything has an opinion" doesn't read well. Also "it's own way" is not very descriptive either, own way of what? Own way of showing things, own way of displaying things or own way of doing things?
So I would probably use something like "there is a way of doing things" and leave it there.