The supernatural force that appoints Donnie to end the alternate universe adopts Frank because Donnie killed him previously. As a manipulated dead, Frank knows what is happening and his job is to guide Donnie on his path to correcting the timeline of the primary universe by returning the jet engine to its original universe; Donnie is unaware of all this.
The costume is necessary because it's an essential part of Frank's character as a dead person (it's what he was wearing when he died) and also because it's so alien (not just some guy), Donnie will understand that he's dealing with things beyond normal.
As far as the costume being a creepy bunny, there is no significance in that. Frank was an artist and it was something he was rendering out when we see him in the ending scenes. It just adds a freaky ambiance is all.
Update: This article has some interesting suggestions on how you could interpret the Rabbit costume
What does the rabbit mean? That depends on how you interpret the
movie. If you think that the film is a serious exploration of
physical/metaphysical reality, you're apt to see Frank as a kind of
rabbit-angel. His role is to guide a reluctant hero into becoming the
instrument of God. In this reading, God wishes to save earth, and
unfortunately (or not) this entails getting Donnie to commit criminal
and destructive acts. Within this context, Frank's ugliness might be
explained as the destructive side of salvation. Perhaps he is a
monstrous rabbit in order to suggest that Donnie himself must become
both prey/ victim and a kind of spiritual predator.
If you follow the parallel-universe theme but do not like the
religious reading, you might see Frank as simply analogous to the
White Rabbit from Alice in Wonderland. The White Rabbit had some
scheduling concerns ("I'm late, I'm late, for a very important date")
and led Alice down to a bizarre alternative world. Like the White
Rabbit, Frank is under time constraints, having only 28 days to get
Donnie with the program. And when he first leads Donnie out to the
local golf course, scene of Donnie's first vision of him, one could
say that Frank has inserted Donnie into the spiral of a new time/space
dimension, just as the White Rabbit did for (to) Alice. In short,
rabbit hole in Alice in Wonderland is wormhole in Donnie Darko, and
both access a new reality.
If you're inclined to see Donnie as just a very disturbed teenager,
then Frank is a tad more malicious. He embodies the dark, destructive
side of Donnie, imagined as the flip side of the rabbit stereotype:
ugly instead of cute, bizarre instead of familiar, destructive instead
of reproductive, and so on. In this reading, Frank stands not just for
the evil side in Donnie but in all of us.