I had parasites, so maybe I can answer this question.
I believe that a parasite cleanse should be done before fasting. Not all cleanses are the same, I believe Humaworms and Barefoots are the best. I like Barefoots protocol (of taking 1 dose each week) for keeping them at bay (having parasites return in force every 4 months is not so good).
Most important part about parasites is not eating/drinking chemicals that allow parasites to breed and to live in organs they shouldn't. For example, many processed foods have wood alcohol in them because they clean the packaging equipement with it. (See any Hulda Clark book for references).
Will fasting help? Sure it will. It won't help killing the parasites but it will help to eject all of the toxins in your body that are keeping them there and infesting parts of your body where they shouldn't be allowed to go.
Depends on what you mean by fast also. If you mean drinking only distilled water the entire time, no food, no supplements, nothing enters your mouth except water, then yes.
I also found a fruitarian diet helped a lot, but I had Candida as well.
Make sure you aren't overdosing on herbs trying to kill the parasites. Not only will ODing on them not help, but it will also make the parasites immune after a while and you might need to take 3 months off all herbs and live with it.
If you're interested in parasites, I'd buy the book " The Cure For All Diseases ". In it, she details exactly what foods tend to breed parasites and what you can do to get rid of them. If you have a real problem, you could also use a zapper every 4 months as well, but if you're not injesting stuff like propyl alcohol, it shouldn't be a problem.