“Interfere,” the term you use most often, carries a negative connotation and implies that the action taken tends to oppose what was already in place. In this sense it is not possible for God to “interfere” in his own divine plan as he would not oppose himself. He does, however, actively participate within his own creation, as most prominently evidenced by the Incarnation.
Many tragic events occur due to the free choices of people (e.g. terrorist attacks), while others, it could be argued, were set in motion by God. I cannot say if God is standing over the universe and is dropping hurricanes and tornadoes down while time progresses or if they are simply the natural result of his work at the moment the universe was created. This distinction may be more semantic than substantive, but God is essentially the source of the “natural” tragic events.
As noted above, only the devils interfere. Angels and saints participate and influence as they understand such actions to be the will of God. All three types of beings, devils, angels and saints, possess free will. The first have chosen to exercise their free will to oppose the will of God, while the latter two are pledged to support it.
Our free choices can certainly be swayed by any supernatural/preternatural influences that may have been brought to bear, the same as by any “natural” or material influences. No supernatural force has the power to overcome our free will any more than do natural or material forces. Whether individual souls are judged “suitable” for heaven or hell depends on whether they are stained by mortal sin for which they have refused to repent.