Here's a small summary about the numbers with many examples: https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf

I also wrote a program in PostScript to draw Cistercian numbers (which uses the nonstandard sign for 6):

  % Specify a four-digit number as the command-line argument.
  /A ARGUMENTS 0 get def
  
  /Digit {
    get 48 sub {
      {} %0
      {24 0 rlineto} %1
      {0 -24 rmoveto 24 0 rlineto} %2
      {24 -24 rlineto} %3
      {0 -24 rmoveto 24 24 rlineto} %4
      {24 0 rlineto -24 -24 rlineto} %5
      {24 -24 rlineto -24 0 rlineto} %6 (nonstandard)
      {24 0 rlineto 0 -24 rlineto} %7
      {0 -24 rmoveto 24 0 rlineto 0 24 rlineto} %8
      {24 0 rlineto 0 -24 rlineto -24 0 rlineto} %9
    } exch get exec stroke
  } bind def
  
  4 setlinewidth
  6 6 moveto
  gsave
    36 0 rmoveto
    0 72 rlineto
    gsave
      -1 1 scale
      A 2 Digit
    grestore
    A 3 Digit
  grestore
  36 72 rmoveto
  1 -1 scale
  0 72 rlineto
  gsave
    -1 1 scale
    A 0 Digit
  grestore
  A 1 Digit
  
  showpage quit

The whole thing is a lot of fun, feels like a Myst puzzle. Or more accuratly, I don't think Myst had a number puzzle but Riven did and I recently picked up Obduction and it had one, So probably fairer to say a Cyan type puzzle as they appear to love creating wierd numeric representations.

1. 5 is the symbols for 4 and 1 combined, 6 is new, then 7=6+1, 8=6+2, and 9=6+3. It seems to me it would be more obvious to have 1 to 5 be unique symbols, then 6=5+1, 7=5+2, 8=5+3, and 9=5+4. Like how we do with tally marks.

2. The system is really just 4 digits combined in a square. I don't see the advantage over Arabic numerals.