I looked at this code briefly a few times, and each time got afraid after being lost in the countless redundant bit tests, and decided I would come back later.
But I finally decided to make a flowchart based on your code (next time, you should make a flowchart first, and make your code based on that). It has some issues. I have highlighted the affected areas (see attachment below).
1: You say you are putting 5V DC into each of the A0, A1, and A2 inputs, and it never activates. Well, yes, according to the flowchart, after the Start, it tests A0, sees a 1, delays, tests A1, sees a 1, delays, tests A1 again, still sees a 1, and goes back to Start. So your program is behaving exactly as expected with those inputs producing no output.
2: Blue - You test A1 twice in a row. Your comments lead me to think you actually meant to test A2, but your code does A1 again.
3: Green - You test A0 twice in a row. Although there is maybe a 0.000001% chance that you could actually make that pin change states between the two tests, why test it twice?
4: Yellow - The A1 tests are mutually exclusive. The first one says if A1 is 0 then reset, otherwise continue. The second one says if A1 is 1 then reset, otherwise continue. Again, it's going to be next to impossible to switch states that fast, so this is an obvious error.
5: Why is it such a long path to get through the right side of the chart? Say that you test A0, get a zero, and wait. Then you test A1 get a 0 and wait. Why then do you test A0 and A1 two more times? While it is definitely possible for them to change states after 0.2 seconds, why test again and again, when you already just tested them?
6: I just noticed another possible mutually exclusive condition after I made the picture, so it's not colored in. The first test of A0 right after Start enters the right hand side when A0 is 0. From here, it only makes it to the Alarm section if it turns to 1 within 0.2 seconds (4 x 50ms delays). You would have to know exactly when it enters this branch of the program, and you would have to toggle it pretty darn quick if your reflexes are even that good.
7: Lastly, if you want to see if your alarm output B output will work (it should), set A0 = voltage, A1 = ground, and A3 = ground. This should allow it to enter the Alarm loop and stay there. You should be able to see the output on B0. After confirming this, change A3 to voltage. At this point the program will loop back to reset. You may see B0 briefly flicker at this point, or it may be too fast to see, but it keeps looping to Alarm and Reset. At this point put A1 = voltage. You should now be in the small loop in the left hand side of the chart that was described in issue 1. If at this point you set A0 to ground, the states it flows to are pretty much irrelevant in their present form.