Q1 :what does "make him almost neat"here mean? innocent?
"Now explain to me. What offense was your brother hauled down to headquarters for?" He made Mason's trip to the office sound like a detective story.
"He spit in everybody's juice."
"That would make how many cups?"
"Twenty they said."
"Twenty. Who would have thought the young lad had so much spit in him!" He laughed. "I'm quoting Shakespeare, sort of."
Vinnie giggled. She couldn't help it. She wasn't sure who Shakespeare was, but Mr. Clayton made Mason sound almost neat.Q2: is "Who would have thought the young lad had so much spit in him"a quotation of Shakespear? what does the original line look like? does this sentence mean: nobody expect such a little child has so much spit?

Question

Q1 :what does "make him almost neat"here mean? innocent?
"Now explain to me. What offense was your brother hauled down to headquarters for?" He made Mason's trip to the office sound like a detective story.
"He spit in everybody's juice."
"That would make how many cups?"
"Twenty they said."
"Twenty. Who would have thought the young lad had so much spit in him!" He laughed. "I'm quoting Shakespeare, sort of."
Vinnie giggled. She couldn't help it. She wasn't sure who Shakespeare was, but Mr. Clayton made Mason sound almost neat.Q2: is "Who would have thought the young lad had so much spit in him"a quotation of Shakespear? what does the original line look like? does this sentence mean: nobody expect such a little child has so much spit?

Answer

Question 2: Here's the full original quote: "Out, damned spot! Out, I say!—One, two. Why, then, ’tis time to do ’t. Hell is murky!—Fie, my lord, fie! A soldier, and afeard? What need we fear who knows it, when none can call our power to account?—Yet who would have thought the old man to have had so much blood in him."

In this scene, Lady Macbeth is feeling guilt for crimes she committed earlier in the play. She believes she sees blood and cannot remove it. "Out, damned spot!" is actually one of the most famous lines in the play.
In the book, however, the man is quoting Shakespeare ironically. He does not believe the boy could possibly have spit into twenty cups.

Question 1: "neat" is an older word for "cool" or "interesting." So she is saying that normally Mason was not very interesting, but because of the way Mr Clayton is talking about him, Mason almost seems cool or interesting.

Answer

If this is a Perry Mason novel, I'm guessing it is U.S. 1960's slang for "wonderful, terrific", synonyms "cool", "groovy".
Neat = Informal sense of "very good" first recorded 1934 in U.S. English.
With the prefix "almost", it would perhaps mean "almost terrific" (but not quite, I guess).

Answer

"neat" here is colloquial.  It means "cool" or "impressive".

"spitting" is associated with feelings of disgust or is a method of insulting someone.  "spit" is also used here as a noun for saliva, the liquid expelled from your mouth when spitting.  So, it probably means that they were surprised that a child had so much saliva in his mouth that he could spit so much.

If you look up the "nofearshakespeare" website, you should be able to find verses which include the word "spit".  I suspect that Shakespeare's characters spat as an insult.

Answer

Spit means mouth, talking, maybe even attitude