God (or the Lord) Works in Mysterious Ways
Though true in a theological sense—how can we say that we understand the true nature of God?—neither this line nor anything like it appears in Biblical text. It's likely appropriated from a hymn, the original line saying that “God moves in mysterious ways.”
Ask and it will be given to you.
This is Luke 11:9 taken entirely out of context. Christ explained that if you asked for forgiveness then it would be given. Sadly some people, including church leaders, use the line to justify high expectations.
God will not give you more than you can handle.
This gem (paraphrased from 1st Corinthians) is used a lot in rehab and therapy programs. Unfortunately its full context may make it invalid for that purpose: it originally states that God will always offer a way out of temptation but it's still on you to take it.
Those whom God wishes to destroy, he first makes angry.
You could argue that there are instances of this being true in Biblical stories, but it isn't explicitly stated in the Good Book. It's wrongly attributed to Euripides when in reality it's a take-off of many, many old proverbs
Patience Is A Virtue
The line itself comes from a 1300s poem. However, the poem is rooted in theology: the book of Galatians makes reference to the “fruit of God's spirit.” One of said fruits is “longsuffering,” sometimes translated as patience, so this one is the closest to being accurate.