Regarding your first question, is it offensive to think of Krishna's Pastimes while chanting, I think you should know that it is not offensive, but rather it is required. One must try for the point when he simply hears Krishna and immediately all of Krishna, His Pastimes, His Form, His Quality, are in his thoughts. So to always be immersed in thoughts of Krishna this is our process. When we are full in Krishna then where there can be any chance for maya in us? So this is our duty to remember Krishna's Pastimes. One who cannot remember Krishna, let him always hear Hare Krishna and then when he has perfected this art, then always he will remember Krishna, His Activities, His Qualities, etc.
The answer to your second question is that when one becomes accustomed to inoffensive chanting, then his fruit is that he is promoted to the stage of pure Love of Godhead, or prema. This prema is the perfectional stage of consciousness and the most blissful by very far.
So far as singing of the Christian hymns, if others sing this we have no objection, it is very nice, but in these hymns they have no definite idea of what is God. We are directly approaching and praying to Krishna for the highest benediction of eternal devotional service so we do not require to repeat the Christian hymns. Our point is to always follow the example of the acaryas and this will bring us to the perfectional stages with no doubt. For the Christian hymn you describe, the example may be given of where one person is appreciating that water is very nice and another is tasting water. So when we taste water the appreciation automatically is there and when we have taste for chanting, automatically the appreciation is there for God.