Mr B,
Elevator Mike is known here for helping others, not being arrogant. His advice to you was very sound. If you had gone to "Learn PLCs", then clicked on "The Internals", you would have seen a diagram that shows the very memory that you asked about.
From your questions, we can tell your level of knowledge. My question now is, "Do you have enough knowledge to understand the information on "Learn PLCS"?", or should you start at a lower level?
(1)As has been pointed out, so-called User Memory is that part of CPU memory that is set aside for use by the user, where Program Memory is reserved for use by the CPU (microprocessor) to store the program and other information used by the CPU.
(2)To calculate the size of User Memory you need, you have to add up all the different requirements of your program. Each ladder rung takes X bytes. Each Input and Output takes X bytes. Each subroutine takes X bytes. Each memory variable (timers, counters, integers, floating numbers, binary numbers, and so on) takes X bytes of memory. Your manuals will give the requirements for each one. Do most of us do this for every project? No, we know from experience approximately what size CPU will be needed for a given program. I have only ran out of user memory 1 time in 30 years, and that was for a program that had 10 inputs and 1 analog output.
(3)Controller tasks refers to the operations performed by the Central Processing Unit (CPU, or the microprocessor), which is the "controller", or brain, in a Programmable Logic Controller. Controller tasks cover a wide range of activities, but the basic processor cycle is very small. Again, refer to "Learn PLCS" ("How It Works") on this site. It consists of only 3 steps: Load Data, Perform Operation, Save Results to Memory. This becomes the scan cycle that Phil Melore mentions in "Learn PLCS".
ALso Mr. B, would you please learn to spell "would", "what", "you are", and a few other English words? It would help to prevent irritation if you could get closer to the right spelling. You may use a spell checker program to help you out with this task.