When I try to open, mono-develop on Unity (on my mac) the icon shows up on my task bar for a few seconds then disappears. Mono-develop never actually opens. How do I fix that?

Try re-installing Unity or installing a fresh copy of Mac . This may problem may happen because of some registry error in mac or maybe because of corruption. Re-installing Unity may help cause once i had a similar problem like you and then i re-install and now it works fine.And if have started your project then export it as an unity package then after re-installing import the package.