Hi @dragos_andrei_87!
Wow!
This is fantastic! You have put so much hard work and effort into this, and I bet you’ve learnt tons in the process. 
It’s so good, that I want to take my time reviewing it, so I’m going to send you feedback for both exercises separately:
Sum of a Range
Your functionality and web page presentation for the input parameters, and how you’ve used jQuery and DOM manipulation to handle the button clicks to call the calculation and display the complete range AND the sum total, is excellent. 
I’ve thoroughly tested it, and it works for most variations. Unfortunately there is one scenario when the calculation of the sum fails in some cases: reverse ranges (i.e. start > end) when the step is greater than 1 — it works for some step values, but fails to calculate the sum of the range correctly for others. The range itself is always output and printed correctly, it’s just a problem with the calculation of the sum.
I’ve noticed that you seem to have over-complicated the function which calculates the sum, and I’m wondering whether simplifying that will solve it. As the exercise in the course book suggests, why don’t you just pass the array of the range from the range
function into the sum
function and iterate over that, rather than start again from the original input data?
I also think you could improve user-friendliness by making it clear on the web page exactly what the fields Argument 1 and Argument 2 relate to i.e. the start of the range, and the end of the range, respectively.
Otherwise, all the other functionality is excellent, and I particularly like how we don’t need to input negative step numbers i.e. the program automatically converts the step (whatever the interval) into a negative step if the range is a descending one 
While you’re working on updating your program for the points I’ve mentioned above, I’ll review your Reversing an Array part 
This is an excellent mini-project which brings together many aspects of the course, including jQuery. I hope you continue to build on and develop it as you learn more. For example, what would be great at some stage is if you could include functionality to reset the input fields to empty after clicking on the calculate and display total button, so that the user doesn’t have to manually delete their previous inputs to perform the next calculation.