All of this is in the manual or online.
For implicit diff, look for ImpDif under the calc menu.
For a second derivative, after the x,type the number corresponding to the nth derivative.
example: will give the second derivative. Just enter 3,4,5, etc for any other derivatives.
For one-sided limits, if you want right, enter in 1. For left, enter -1.
example: left-sided limit, approaching 0 from the left:
And of course it'll give decimals. Set it to 'approx' mode or just press the green key and then enter.
Look above your ENTER button. Is there a squiggly looking equal sign?. That means approximate.