They play around with the true meaning of words so much it becomes difficult to understand what they really mean, so much for trying to draw close to God.
In the Insight book they acknowledge that the term mediator is the same as intercessor
>>Mediator - One who interposes between two parties at variance to reconcile them; an intercessor; an intermediary agent, or go-between. In the Scriptures the term is applied to Moses and Jesus, the mediators respectively of the Law covenant and the new covenant.—Ga 3:19; 1Ti 2:5.>>
They don't use the term mediator when discussing prayers but use the word intercessor, here is an example from W 02 9/15
<<However, God has appointed an Intercessor for our prayers. “I am the way and the truth and the life,” said Jesus Christ. “No one comes to the Father except through me.” Jesus also stated: “Whatever it is that you ask in my name, I will do this, in order that the Father may be glorified in connection with the Son. If you ask anything in my name, I will do it.” (John 14:6, 13, 14) We can be confident of Jehovah’s willingness to hear prayers offered in Jesus’ name. Concerning Jesus, the Bible says: “He is able also to save completely those who are approaching God through him, because he is always alive to plead [“be interceding,” footnote] for them.”—Hebrews 7:25>>
They teach that Jesus is the mediator between God and the anointed in both the new covenant and the Kingdom covenant and Jesus, in his role as High Priest is the mediator for all JWs in prayer only .
Their play with words and ideas is also evident when it comes to calling God our father. For the other sheep, they can only use this term as an endearment (he is not their father) and not in it's true sense, whereas God is father to the anointed. The W 15 6/15 reconfirms this
<<4 The expression “our Father,” not “my Father,” reminds us that we belong to an “association of brothers” who truly love one another. (1 Pet. 2:17) What a precious privilege that is! Anointed Christians, who have been begotten as God’s sons with heavenly life in view, rightly address Jehovah as “Father” in the fullest sense. (Rom. 8:15-17) Christians whose hope is to live forever on earth can also address Jehovah as “Father.” He is their Life-Giver, and he lovingly provides for the needs of all true worshippers. Those with this earthly hope will in the fullest sense become God’s children after they have reached perfection and have proved their loyalty in the final test.—Rom. 8:21; Rev. 20:7, 8.>>