if needed or if need/If completed or complete

All appropriate:

If needed

If need be

If need to

If needed is correct. It's hard to explain the grammar of it, but I think you can't say if need because it doesn't imply the condition of a subject (i.e., the "to be" verb).

If needed = if it is needed = if rescheduling is needed

"If need" can not be made into "if it is need." You can however say "if there's a need."

Also I don't think you can say "if need to" for the same reasons I described above.