Does the CPU have the same chance to try to improve relationships in the year end tasks as the user does or is it just a user benefit? Also, does not taking any action at this stage cause a negative response or does the transfer likelihood stay the same?

I don't know the innerworkings of the game so can't help you re what the CPU/AI does related to this.

Contacting those who may possibly transfer gives you the chance to influence them..but the results of your efforts may be positive, neutral or negative, depending on the player (attitude, relationships with players and coaches, reasons for possibily wanting to transfer, how firmly set he is re transferring)...and what tack you decide to take when talking with him. I'd say not contacting means his desire to transfer pretty much stays the same, but maybe (not sure) some players might take it as a slight.