Does my concept of God affect how I pray? Yes.
Does a praying life affect my mental health? Yes. The more I pray before the God I understand reduces fear and anxiety.
For some recent empirical research to back up this idea see "Sociologist: Concept of God impacts power of prayer, anxiety-related disorders." Prayer seems effective in combating psychological challenges, like relieving anxiety. The level of effectiveness is connected with the person's concept of God.
Baylor University sociologist Matt Bradshaw received a Templeton Grant and published his findings in the journal Sociology of Religion - "Prayer, Attachment to God, and Anxiety-Related Disorders Among U.S. Adults."
"According to his study, people who prayed to a loving and supportive God whom they thought would be there to comfort and protect them in times of need were less likely to show symptoms of anxiety-related disorders — irrational worry, fear, self-consciousness, dread in social situations and obsessive-compulsive behavior — than those who prayed but did not expect God to comfort or protect them."
Perceived characteristics of God - such as loving, remote, or judgmental - affect the relationship between prayer and mental health.
For the praying person, what we think of God makes a difference.
I write more extensively in chapter 2 of my book Praying - "Praying and the Nature of God."