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Converting a `while loop` to a `for loop` is a common task in programming, particularly when aiming to make code shorter and more readable. A `while loop` in C++ repeatedly executes a block of code as long as a specified condition remains true. Our given original code has a `while loop` that increments a variable `i` from 0 to 20.
In the conversion process, the key elements to consider are:

• Initialization: In the `while loop`, the variable `i` is initialized outside the loop. In a `for loop`, this initialization is embedded within the loop statement itself.
• Condition: Both loop types require a condition to control execution. In this example, the condition `i <= 20` is identical for both.
• Increment: The `while loop` updates the counter variable `i` at the end of its block. The `for loop` integrates this increment (`i++`) into its statement, making loops more streamlined.

Once translated, the `while loop`: ``` int i = 0; while (i <= 20) { // code block i++; } ``` becomes this `for loop`: ``` for (int i = 0; i <= 20; i++) { // code block } ```
The outcome is a loop that is easier to read and maintain, especially as code becomes more complex.

Loop control structures are essential in programming for executing specific blocks of code multiple times. In C++, the primary loop control structures are `for loop`, `while loop`, and `do-while loop`. Each serves distinct use-cases based on different needs of initialization, control, and termination conditions.

• For Loop: Utilized for situations where the number of iterations is known before entering the loop. It initializes, checks a condition, and updates in one concise statement, making it optimal for counting loops.
• While Loop: Ideal for scenarios where the loop should continue until a condition changes, with the condition checked before entering the loop's body. Useful when the number of iterations isn't known in advance.
• Do-While Loop: Similar to the `while loop`, but checks the condition after executing the loop's block, guaranteeing at least one execution of the loop body.

The control structures in loops help programmers determine the exact flow and repetition required for various tasks. They ensure that loops can efficiently handle counting, waiting for a condition to change, or ensuring minimum execution, based on the requirements of the problem at hand.

Conditional statements allow us to make decisions within our loops. This means we can execute different actions based on different conditions. In our example, the loop executes different arithmetic operations based on whether `i` is even or odd, and whether `i` is less than, equal to, or greater than 10.
Here's how it works:

• When `i` is an even number and `i` is less than or equal to 10, the condition `if (i % 2 == 0 && i <= 10)` will add the square of `i` to the `value`.
• When `i` is an even number and over 10, the `else if (i % 2 == 0 && i > 10)` condition is true, and `i` simply gets added to `value`.
• For odd values of `i`, the `else` section subtracts `i` from `value`.

These conditions change the flow of our loop based on dynamically changing data – in this case, the changing values of `i`. This is a powerful technique to handle different cases within a loop, allowing for complex decision-making processes as the loop iterates through each cycle. Understanding how conditional statements work inside loops enables more complex computations and logic flows to be implemented effectively.