Generate code from full name and index number
Your code is quite confusing, are you new to Python? You seem to have some misunderstandings about how it works. First of all, no you don't need sys. Python scripts end automatically when they reach the end. You only need to call sys.exit() if you want to end a script in the middle of it for any reason.

Next, you're calling str on a string that's already a string. Based on the other variables you've defined this might be a placeholder, but it's confusing so it's worth saying that you're using placheolder values. I would also put it in as a number, except that you start the number with 0. An int can't have 0 as its first digit, so either you should be getting that number as a string (removing the need for str()) or there's something else going on here. Also I would suggest that you put the comment on a separate line, to be more readable.

# Converting number to str so it can concat
index_number = str('02001201525')


The from_index function is confusing. The name doesn't tell you what it does. It runs split but there's no need to if you just need the first 5 characters. It also probably shouldn't be a function. It has a very specific seeming use, takes no useful parameters and in the end just returns [0:5] on the string that's passed into it. It's easier to just do this:

index_number[0:5]


The only difference between that and your function is that your function would cut the result short if there was white space in the number, but that doesn't sound like it's what you want.

As for your generate_code, it does work for the most part, but is again a lot of lines to do something relatively simple. It also doesn't take index_number as a parameter even though it really should. I'd actually reduce it to one line, like this:

def generate_code(first_name, last_name, index_number):
    return first_name[-1] + last_name[2:4] + index_number[0:5]


Note that you also put in the wrong parameters to get the second and third parameters of last_name. I'm not sure if it was just a typo or misunderstanding, but I'll explain slicing if you need me to. Just comment and I can write up a bit about it.