Hello native English speakers. This time is for just one sentence but a bit long written by me.

Not Tom but Jack did that task not with any tools but his left hand , not for his boss but for his friends, not in his home but in the open air, not in the morning but at night.
Question: Is this sentence grammatically correct?
By the way, ① If I have removed all of the commas in this sentence, what about the correctness of its grammar? and about its meaning?
② If I deliberately change the order of all the elements which function as adverbial.

(for one example: Not Tom but Jack did that task not in the morning but at night, not in his home but in the open air, not with any tools but his left hand , not for his boss but for his friends.)

is such a sentence also grammatically correct and having the same meaning?

Question

Hello native English speakers.  This time is  for just one sentence but a bit long written by me.

Not Tom but Jack did that task not with any tools but his left hand , not for his boss but for his friends, not in his home but in the open air, not in the morning but at night.
Question:  Is this sentence grammatically correct?
By the way, ① If I have removed all of the commas in this sentence, what about the correctness of its grammar? and about its meaning?
② If I deliberately change the order of all the elements which function as adverbial.

(for one example: Not Tom but Jack did that task not in the morning but at night, not in his home but in the open air, not with any tools but his left hand , not for his boss but for his friends.)

is such a sentence also grammatically correct and having the same meaning?

Answer

I think it mostly works except the phrase "not with any tools but his left hand" 
In my opinion it would need to be changed to "not with any tools, but with his left hand".

A more common way of saying it might be: 'Without any tools except his left hand."  or "With no tool but his left hand."

Removing the commas would create problems.  Actually, I think it needs more commas:

Not Tom but Jack did that task, not with any tools, but with his left hand, not for his boss but for his friends, not in his home but in the open air, not in the morning but at night.

Your punctuation is interesting.  I believe you might be using what is called a comma splice. It's sort of poetic, probably not the sort of thing you'd do for technical writing.

Answer

yes, it's correct and clear, a very fine sentence

no, it's better not to change the order as you will lose the cohesion with previous events mentioned in the text eatlier.