As super means above and para means beyond, I would say the differences lie in the parts natural and normal.
In the mere word sense something paranormal is just beyond normal. Natural can be interpreted as synonym to normal in the sense of something comes natural and the like. It can be interpreted as another realm as well, the realm of God as opposed to the realm of man.
As @Aidas would use paranormal for the mysterious, one could argue that the realm of God is paranormal. But it is very unusual to talk of the realm and the workings of God as paranormal, while it is perfectly normal to call effects believed to be caused by UFO's, aliens (from outer space), or ghosts paranormal.
In addition it seems more fitting to call effects paranormal, while supernatural would also be used for beings.
paranormal is translated into German as übersinnlich, above the sense realm, while supernatural is translated überirdisch, übermenschlich, übernatürlich: above earthly, above humane, supernatural.
Confident is an adjective and overly is an adverb. Adjectives are usually modified by adverbs. This is a perfectly normal and grammatical construction.
The other word is usually written as one word: overconfident.
The meanings are the same.
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Where self-assured is 'sure of yourself,' relates to you and your actions (it also comes with a minor connotation of pride), self-confident is confidence in one's abilities and relates more to your mind.
They may be used interchangeably, (m-w.com defines self-assured as self-confident), but there are minor differences in tone that can affect your reader.