Touch Lua's Draw Library Basics

WARNING: This question is only for Touch Lua users who have purchased and have knowledge of the Draw Library.

PLEASE REFER TO THE BOTTOM PORTION OF THIS QUESTION TO SEE THE FULL PROGRAM. THE SNIPPETS I USE IN THE BEGINNING ARE PART OF THAT PROGRAM (NUMPAD.LUA)

Okay, so now for the questions:

•What's the use of "." between "b" and "x"? Or "b" and "draw"? Etc...

•How does the table set up the button? Please be super specific?

•Why is there a "+", "*", and "(j-1)" in lines 7 and 8?

•What's height and width doing in there? I thought there were only x and y.

function createButtons()
   buttons = { }
   local c = 1
   for i = 1, 4 do
      for j = 1, 3 do
         local b = { }
         b.x = 80 + 60 * (j-1)
         b.y = 160 + 60 * (i-1)
         b.width = 40
         b.height = 40
         b.color = draw.blue
         b.draw = drawButton
         b.action = digitAction
         buttons[c] = b
         c = c + 1
      end
   end
   buttons[1].title = '7'
   buttons[2].title = '8'
   buttons[3].title = '9'
   buttons[4].title = '4'
   buttons[5].title = '5'
   buttons[6].title = '6'
   buttons[7].title = '1'
   buttons[8].title = '2'
   buttons[9].title = '3'
   buttons[10].title = '0'
   buttons[11].title = '.'
   buttons[11].action = dotAction
   buttons[12].title = 'C'
   buttons[12].color = draw.orange
   buttons[12].action = clearAction
end

Lastly, referencing the program as a whole... •How does the button know when you tap on it? Specifically what are the lines of code and how does it work? (I have a very faint understanding of track touches btw)

function digitAction(button)
   if string.len(display.title) < 16 then
  sys.alert('tock')
  if display.started then
     display.title = display.title .. button.title
  else
     if button.title ~= '0' then
        display.title = button.title
        display.started = true
     end
  end
   else
  sys.alert('tink')
   end
end

function dotAction(button)
   if string.find(display.title, '.', 1, true) then
  sys.alert('tink')
   else
  display.title = display.title .. '.'
  display.started = true
  sys.alert('tock')
   end
end

function clearAction(button)
   sys.alert('tock')
   display.title = '0'
   display.started= false
end

function createDisplay()
   display = { }
   display.x = 60
   display.y = 100
   display.width = 200
   display.height = 40
   display.title = '0'
   display.color = draw.red
   display.started = false
end

function createButtons()
   buttons = { }
   local c = 1
   for i = 1, 4 do
  for j = 1, 3 do
     local b = { }
     b.x = 80 + 60 * (j-1)
     b.y = 160 + 60 * (i-1)
     b.width = 40
     b.height = 40
     b.color = draw.blue
     b.draw = drawButton
     b.action = digitAction
     buttons[c] = b
     c = c + 1
  end
   end
   buttons[1].title = '7'
   buttons[2].title = '8'
   buttons[3].title = '9'
   buttons[4].title = '4'
   buttons[5].title = '5'
   buttons[6].title = '6'
   buttons[7].title = '1'
   buttons[8].title = '2'
   buttons[9].title = '3'
   buttons[10].title = '0'
   buttons[11].title = '.'
   buttons[11].action = dotAction
   buttons[12].title = 'C'
   buttons[12].color = draw.orange
   buttons[12].action = clearAction
end

function drawDisplay()
   draw.setfont('Helvetica', 20)
   draw.setlinestyle(2, 'butt')
   local x1, y1 = display.x, display.y
   local x2, y2 = x1 + display.width, y1 + display.height
   draw.roundedrect(x1, y1, x2, y2, 10, display.color)
   local w, h = draw.stringsize(display.title)
   local x = x2 - 10 - w
   local y = y1 + (display.height - h)/2
   draw.string(display.title, x, y, draw.black)
end

function drawButton(b)
   draw.setfont('Helvetica', 18)
   draw.setlinestyle(2, 'butt')
   local x1, y1 = b.x, b.y
   local x2, y2 = x1+b.width, y1+b.height
   draw.roundedrect(x1, y1, x2, y2, 10, b.color)

   local w, h = draw.stringsize(b.title)
   local x = b.x + (b.width - w)/2
   local y = b.y + (b.height - h)/2
   draw.string(b.title, x, y, draw.black)

end

function drawButtons()
   for i = 1, #buttons do
  buttons[i].draw(buttons[i])
   end
end

function lookupButton(x, y)
   for i = 1, #buttons do
  local b = buttons[i]
  if x > b.x and x < b.x+b.width and y > b.y and y < b.y+b.height then
     return b
  end
   end
   return nil
end

function drawScreen()
   draw.beginframe()
   draw.clear()
   drawDisplay()
   drawButtons()
   draw.endframe()
end

function touchBegan(x, y)
   local b = lookupButton(x, y)
   if b then
  b.action(b)
   end
end

function touchMoved(x, y)
end

function touchEnded(x, y)
end

function init()
   draw.setscreen(1)
   draw.settitle('Num Pad')
   draw.clear()
   draw.tracktouches (touchBegan, touchMoved, touchEnded)

   createButtons()
   createDisplay()
end

function mainloop()
   while true do
  draw.doevents()
  drawScreen()
  draw.sleep(30)
   end
end

function main()
   init()
   mainloop()
end

-- start program
main()

Thank you so much for any help you can offer! I know this is a lot of questions, but this knowledge can really help propel me forward!