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, and so on.

[Srila Prabhupada; letter to Sivananda, Los Angeles, 4 December, 1968]

Generally it is the process to simply chant and hear, but if Krsna’s lila comes into remembrance, that is very good. It should come automatically. Not that you are remembering artificially.

[Srila Prabhupada, letter to Prahladananda, Bombay, 17 June, 1971]