If both of you feel like it was wrong to separate or if you miss each other, then by all meas, but if you are only returning to each other because of familiarity, do not. Familiarity brings the problems back, while actually missing them can help you realize where you were wrong and try to fix the flaws you previously had.
Only if they want to. Sometimes it might work. It will never work if either of them keeps on mentioning or asking about relationships they had while apart. To be together again they each might have to drop a few friends.
Ignorant people still want to ask me about my breakup with my ex. I start to cry and say everything was OK until she ran off with that circus clown. LOL
Possibly. Imagine you had a chance meeting with your boyfriend/girlfriend from when you were 18, 25 years or more since you last saw one another... you'd both have changed a lot since then, but maybe you both still have those characteristics that made you attracted to each other. Who knows - it might work out.
Whats to 'believe in'? There can be countless reasons why or why not folks should be together, whether they have done it before or not. We can't know what is happening/has happened in a pair of lives that would bring them to such a decision, though we can hope that it isn't a fear response; 'better the devil you know than the one you don't' as it were. Wish them well, move on...
I think people break up for a reason. Perhaps time lets us discover that reason then was less than perfect. So my answer is that it depends on the two people. Maybe it wasn't the right time the first time around. So yes, if two people find their back to each other, it is worth a second chance.