The full name of the document is Last Will and Testament. One definition:
A document in which a person specifies the method to be applied in the management and distribution of his estate after his death.
Will is a common term to refer to this document. I wouldn't call it informal; I think it's what people use most of the time. In a legal context you're probably better off using the full name, though.
The comments on your question seem correct to me - that the word "ever" is used to enhance the meaning of "since".
There are some distinctions I would make:
Ever since that day, he has been like a different person.
This implies that something happened on that day that changed him, and he has been acting differently every day, consistently, between then and now.
Since that day, he has become a different person.
With "since", and no "ever", I can write a sentence that implies that he has changed somehow between then and now, but I don't say when. He could have changed three days after "that day", or it could have been yesterday. (This sentence also implies that the change happened because of some reason unrelated to "that day".)
Additionally, the word "ever" can be used to differentiate "since" from its other meaning, as a synonym for "because". Consider:
Since she started wearing purple, he has been wearing blue.
This could mean either that he started wearing blue because she started wearing purple, or that he started wearing blue after she started wearing purple, for reasons unconnected.
Ever since she started wearing purple, he has been wearing blue.
This sentence can only have the second meaning - that his wearing blue started after her wearing purple, but not necessarily as a result of it.
Best Answer
I believe both sentences are correct and mean the same thing. I assume that all day is a more common expression than all the day.
Yes, Google Books confirms it.
In addition, there is a very good answer on ELU given by @Sven Yargs. I will cite the paragraph which summarises the difference between these two in modern English.
The original quote by Charles Kingsley also has long at the end, which slightly emphasises all day.