Now that Pope Benedict has stepped down, does he remain
infallible? If so, how might that conflict with the infallibility of
the next incumbent?
The pope is infallible when, as head of the bishops of the church, he requires the faithful to believe a matter pertaining to faith or morals.
This is the standard definition of infallibility. It goes no further.
Should the pope stick his head out of doors and remark that it will be a nice day, he is just as liable to be snowed on as the next man.
In practice, this means that the church debates a subject at great length and when the bishops and laity are in agreement, the pope makes an infallible pronouncement.
The bishops' discussions before the announcement can take a long time; the doctrine of the immaculate conception was in debate for at least 1,300 years before being made official.
The pope, then, is analogous to the head of any company; he will say what his board of directors tells him.
In the case of Emeritus Pope Benedict, the exercise of infallibility will not be required, since he is no longer in charge.
Pope Francis is unlikely to have to be called upon, because there is nothing significant in the pipeline, as far as I know.
Any other pronouncements the pope may make will be to do with organisational matters such as married priests, contraception and the like, which are liable to change because they are man-made rules promulgated in the best knowledge of their time.
He will not be infallible when he makes such pronouncements, so just think of the pope as Mr Chairman and relax.