Can I access individual pixels on my 16x2 LCD display
It's possible to define custom characters for “generic 16x2 LCD displays” [ie, displays based on HD44780 or equivalent controllers], but only up to eight such characters at the same time.  See LiquidCrystal.CreateChar for details.  See page 2 and part of page 1 of the Print degree symbol ° on LCD arduino.cc thread for create-character examples that don't use the library.  Page 1 of that thread also shows a table of all the characters built into typical HD44780 controllers, some of which may perhaps meet your needs.

For pixel-by-pixel LCD control, look at graphics LCDs, eg the KS0108 or LCD12864 and similar.