Plot voltage for different resistor values in LTSpice
Why is the current displayed as a curve? Is it because the R = 1 + 100
  * time expression is incorrect?


The time is increasing from 0 to 0.1, at 0 time the resistor is 1Ω. When the time reaches the end of the simulation it is R = 1+100*0.1 which is equal to 11 ohms

V/R = I so the relationship would be 1/x which is a function that looks like this:



  How can i model a real voltage source and current source in SPICE?


A real voltage source has source resistance (and maybe some inductance) and cannot provide infinite current. 


  In LTSpice there's a current component as well. Are the Current and
  Voltage components models of ideal voltage and current sources or real
  voltage sources


They are ideal, they provide infinite current or  infinite voltage. A real source cannot do this and can't provide current instantaneously.


  How would I do to create a simulation that would display a graph
  resistance vs voltage graph as in the book example at the top of this
  post?


See this post: 
How do I achieve XY mode on LTspice?

You can also use equations in the graphing window, pressing alt after simulation gives you the power for the component, and there is a way by holding down the voltage probe and dragging to get a differential signal.