In dimensionless analysis, coefficients of quantities which have the same unit for numerator and denominator are said to be dimensionless. I feel the word dimensionless is actually wrong and should be replaced by "of dimension number". For example, the Mach number is of dimension one. 

Many people write, for this case: 


  Mach-Number | Dimension: "-" | Unit: "1"


As mentioned before, I would say 'Dimension: "1"' in this place. But what about the unit? $\text m/\text s$ divided by $\text m/\text s$ is equal to one. But is the number one a unit by definition? Or should one say that the Mach number has no unit and therefore 'Unit: "-"'?


Question: What to do about students who ask for help too often?
Answer: It looks like you have two different issues, it's easiest to discuss each of these separately.


Students will bring me some plagiarized work, showing it to me early,
as a sort of test if I will notice. It seems difficult to punish
plagiarism when the paper is not yet submitted.


This one is rough. You can't punish someone due to plagiarism before they submit work. The best policy, in my opinion, is twofold. 

First - if a student brings plagiarized work then you should simply say "I'm sorry, I cannot help you with work that is not your own." and point to you university's policy regarding academic dishonesty. Repeat offenders should be put on notice.

Second - If you grade the final assignments or are involved consider spending a bit more time plagiarize-checking these particular student's submissions. These students have shown that they were willing to claim other's work as their own, being a bit more stringent in checking their work for originality is, in my opinion, completely fair.


Students will bring in papers again and again, with little changes
put in at each stage, hoping their minimal effort each time will be
sufficient to reach their goal of a "D".


This sounds like a communication problem. After meeting with a student there should be no confusion about what will improve the student's work. For something like a paper it should be "In order to improve this paper you should: extend the intro, go into more detail here, etc" Students returning for additional assistance should have some sort of checklist that they should complete prior to returning for more assistance. Make this clear and obvious and, if there are multiple tutors a student could work with, something that is kept in some sort of notes system.