So my party is split on this. One of my group members believes that I can’t use stillness of mind to end a frighten special effect that says I must use my action to do something. If the special condition of the frighten says I need to take an action to run until I’m safe, am I not allowed to end the frighten? This doesn’t seem correct to me. Can you guys help me clarify?

If a game effect says you have to spend your action doing a certain thing, then you have to spend your action doing that thing.

If you're talking about the Fear spell, taking the Dash action using your bonus action is sufficient and would leave your action free to use Stillness of Mind. The spell doesn't actually require you to spend your action, as long as you take the Dash action somehow.

So if I am charmed from suggestion, I can’t get rid of the suggestion but only the charm actual condition? It seems sort of underpowered then. 

1. Suggestion doesn't charm you.
2. Stillness of Mind ends the whole effect, not just the condition.
3. The crux of the matter is that you can only use Stillness of Mind if the effect that's frightening or charming you doesn't prevent you from using your action on Stillness of Mind.

Perfect! Thanks for the clarification! Not sure why  this confused me so much.