Explanations

AMAZING= Incredible, fantastic, wonderful, awesome, great.

GRACE= Divine love and protection bestowed freely on people. The state of being protected or sanctified by the favour of God.

WRETCH= A miserable, unfortunate, or unhappy person. A person regarded as base, mean, or despicable.

A WRETCH LIKE ME= Me, who am a wretch. (I'm a wretch and you saved me)
If I say "I don't want to talk to liars like you", I'm saying that you are a liar and I don't want to talk to you.

'TWAS= (a bit old fashioned) It was.

TO FEAR= To be afraid. (a Christian must be afraid of all the things that may harm their soul)

RELIEVE= To free from pain, anxiety, or distress. To rescue.

PRECIOUS= Valuable, dear, cherished, important, of high value, very much loved.

DID= An exclamation doesn't need inversion, so we say "How precious you are", "How precious your grace appeared". When we use DO in an affirmative sentence (and this sentence is affirmative, not a question) we use it for emphasis, to give more importance to the verb, so in this sentence DID is emphasizing the verb APPEAR.

SET FREE= Liberated, made free.

MY GOD, MY SAVIOUR= Jesus (who is God and saved us from eternal death)

RANSOMED= The release of property or a person in return for payment of a demanded price. In Christian faith, to ransom is to deliver from sin and its consequences, because Jesus died to make us free from sin and its chains (if we accept), so we say that "Jesus ransomed us" (He paid the price that we needed to pay to clean our many sins).

FLOOD= /flʌd/ An abundant flow or outpouring of water (also figuratively, of love, grace, etc.)

REIGNS= Rules, govern (in the way a king rules)

UNENDING= Neverending, everlasting, eternal.