Interpret loose ranges
Python 2 - 239 211 210 bytes

Thanks to @mbomb007 and @Cyoce for further golfing this solution!

def r(s):
 t=[]
 for x in s.split("AND"):
  if"T"in x:a=map(int,x.split("TO"));b=2*(a[0]&lt;a[1])-1;t+=range(a[0],a[1]+b,b)
  else:t+=int(x),
 return t
lambda p,v:[(['']+p+['']*max(map(abs,r(v))))[x]for x in r(v)]


Straight-forward approach. Tried generators and a recursive version, but they couldn't beat the simple for each loop. I'm a golfing noob, so this can most likely be improved quite a bit. Also, the major flaw of this snippet is that the range as a list object is computed again each time an element is retrieved from the character array (see last line, list comprehension). This means r(s) is executed len(r(s)) + 1 times.

Ungolfed code:

def find_range(string):
    result = []

    # Split at each AND and look at each element separately
    for element in string.split("AND"):
        # Element is just a number, so add that number to the result list
        if "TO" not in string:
            result += [int(string)]

        # Generate a list with all the values in between the boundaries 
        # (and the boundaries themselves, of course) and append it to the result list
        else:
            boundaries = map(int, string.split("TO"))
            ascending = boundaries[0] &lt; boundaries[1]

            # range(start, stop, step) returns [start, ..., stop - 1], so extend the stop value accordingly
            # range(8, 3, 1) returns just [], so choose respective step (negative for a descending sequence)
            result += range(boundaries[0], boundaries[1] + (1 if ascending else -1), 1 if ascending else -1)

# Make the char array 1-indexed by appending an empty char in 0th position
# Add enough empty chars at the end so too large and negative values won't wrap around
interpret = lambda chars, range_expr: [(['']+chars+['']*max(map(abs, find_range(range_expr))))[x] for x in find_range(range_expr)]


Test cases:

c = list("Hello World")
print interpret(c, "1 TO 3")
print interpret(c, "5")
print interpret(c, "-10 TO 10")
print interpret(c, "0 AND 2 AND 4")
print interpret(c, "8 TO 3")
print interpret(c, "-300 AND 300")


Output:

['H', 'e', 'l']
['o']
['', '', '', '', '', '', '', '', '', '', '', 'H', 'e', 'l', 'l', 'o', ' ', 'W', 'o', 'r', 'l']
['', 'e', 'l']
['o', 'W', ' ', 'o', 'l', 'l']
['', '']