This answer is very similar to Brian's answer, but a little bit sanitized and the output has no duplicates:
words = ["Words", "Shirt", "Blouse", "Sweater"]
md = {"e": "q,w", "a": "z"}
md = {k: v.split(',') for k, v in md.items()}
newwords = []
for word in words:
    newwords.append(word)
    for c in md:
        occ = word.count(c)
        pos = 0
        for _ in range(occ):
            pos = word.find(c, pos)
            for r in md[c]:
                tmp = word[:pos] + r + word[pos+1:]
                newwords.append(tmp)
            pos += 1
Content of newwords:
['Words', 'Shirt', 'Blouse', 'Blousq', 'Blousw', 'Sweater', 'Swqater', 'Swwater', 'Sweatqr', 'Sweatwr', 'Swezter']
Prettyprint:
Words
Shirt
Blouse
Blousq
Blousw
Sweater
Swqater
Swwater
Sweatqr
Sweatwr
Swezter
Any errors are a result of the current time. ;)
Update (explanation)
tl;dr
The main idea is to find the occurences of the character in the word one after another. For each occurence we are then replacing it with the replacing-char (again one after another). The replaced word get's added to the output-list.
I will try to explain everything step by step:
words = ["Words", "Shirt", "Blouse", "Sweater"]
md = {"e": "q,w", "a": "z"}
Well. Your basic input. :)
md = {k: v.split(',') for k, v in md.items()}
A simpler way to deal with replacing-dictionary. md now looks like {"e": ["q", "w"], "a": ["z"]}. Now we don't have to handle "q,w" and "z" differently but the step for replacing is just the same and ignores the fact, that "a" only got one replace-char.
newwords = []
The new list to store the output in.
for word in words:
    newwords.append(word)
We have to do those actions for each word (I assume, the reason is clear). We also append the world directly to our just created output-list (newwords).
    for c in md:
c as short for character. So for each character we want to replace (all keys of md), we do the following stuff.
        occ = word.count(c)
occ for occurrences (yeah. count would fit as well :P). word.count(c) returns the number of occurences of the character/string c in word. So "Sweater".count("o") => 0 and "Sweater".count("e") => 2.
We use this here to know, how often we have to take a look at word to get all those occurences of c.
        pos = 0
Our startposition to look for c in word. Comes into use in the next loop.
        for _ in range(occ):
For each occurence. As a continual number has no value for us here, we "discard" it by naming it _. At this point where c is in word. Yet.
            pos = word.find(c, pos)
Oh. Look. We found c. :) word.find(c, pos) returns the index of the first occurence of c in word, starting at pos. At the beginning, this means from the start of the string => the first occurence of c. But with this call we already update pos. This plus the last line (pos += 1) moves our search-window for the next round to start just behind the previous occurence of c.
            for r in md[c]:
Now you see, why we updated mc previously: we can easily iterate over it now (a md[c].split(',') on the old md would do the job as well). So we are doing the replacement now for each of the replacement-characters.
                tmp = word[:pos] + r + word[pos+1:]
The actual replacement. We store it in tmp (for debug-reasons). word[:pos] gives us word up to the (current) occurence of c (exclusive c). r is the replacement. word[pos+1:] adds the remaining word (again without c).
                newwords.append(tmp)
Our so created new word tmp now goes into our output-list (newwords).
            pos += 1
The already mentioned adjustment of pos to "jump over c".
Additional question from OP: Is there an easy way to dictate how many letters in the string I want to replace [(meaning e.g. multiple at a time)]?
Surely. But I have currently only a vague idea on how to achieve this. I am going to look at it, when I got my sleep. ;)
words = ["Words", "Shirt", "Blouse", "Sweater", "multipleeee"]
md = {"e": "q,w", "a": "z"}
md = {k: v.split(',') for k, v in md.items()}
num = 2     # this is the number of replaces at a time.
newwords = []
for word in words:
    newwords.append(word)
    for char in md:
        for r in md[char]:
            pos = multiples = 0
            current_word = word
            while current_word.find(char, pos) != -1:
                pos = current_word.find(char, pos)
                current_word = current_word[:pos] + r + current_word[pos+1:]
                pos += 1
                multiples += 1
                if multiples == num:
                    newwords.append(current_word)
                    multiples = 0
                    current_word = word
Content of newwords:
['Words', 'Shirt', 'Blouse', 'Sweater', 'Swqatqr', 'Swwatwr', 'multipleeee', 'multiplqqee', 'multipleeqq', 'multiplwwee', 'multipleeww']
Prettyprint:
Words
Shirt
Blouse
Sweater
Swqatqr
Swwatwr
multipleeee
multiplqqee
multipleeqq
multiplwwee
multipleeww
I added multipleeee to demonstrate, how the replacement works: For num = 2 it means the first two occurences are replaced, after them, the next two. So there is no intersection of the replaced parts. If you would want to have something like ['multiplqqee', 'multipleqqe', 'multipleeqq'], you would have to store the position of the "first" occurence of char. You can then restore pos to that position in the if multiples == num:-block.
If you got further questions, feel free to ask. :)