I think that you must be
I come from a place way out of town.
astro - relating to outer space
Yet I only have fake friends when I’m on the ground.
To astroTurf - turf being ground - is the tactic of creating the appearance of grassroots support for a position, which are fake friends, masking the real sponsors.
If I fall, I will not be able to hold it in.
Gastro - g for gravity (the fall) - is short for gastroenteritis, where food can't be held in.
Twice, and I might just have to run back home.
Astros - the plural, refers to the Houston Astros, a MLB team, who run to reach home.
But I’m not simply a wanderer in the dark.
Astronaut - naut sounds like not/naught - is a wanderer in space.
See, I can become a powerful leader!
Castro - adding C (see) gives the Cuban leader/s
I can even tell the future using a mathematical function.
astrology - to predict the future, by adding $\log y$
And if you dare rile me up, I’ll put you down.
roast - the anagram, meaning to severely criticize
You might find me in Greece when I run back home. -
Astros, a town in Arcadia, Greece.
If you rile me up again, I'll be square with you.
Sator/Rotas, anagrams found in the Sator Square
S A T O R
A R E P O
T E N E T
O P E R A
R O T A S
Title: I’m there when everything goes wrong
catastrophe contains astro