The Sages prohibited starting a task or a meal during the half hour before the time of bedikat ḥametz, out of concern that one might become caught up in these activities and forget to search for ḥametz. It is permitted, however, to snack on fruit or pastry, or to perform light work that can be finished quickly.
Once the time for bedika arrives, it is improper to start any sort of work or eat fruit, even as a quick snack, for it might impede the fulfillment of the mitzva at its proper time (BHL §431).
One should not begin studying Torah once the time for bedikat ḥametz has arrived. If one began studying Torah beforehand, some poskim rule that he may continue studying (Beit Yosef), but according to many poskim, even in this situation it is best to stop studying at tzeit ha-kokhavim, in order to fulfill the mitzva of bedikat ḥametz at its proper time (MB 431:11; Kaf Ha-ḥayim ad loc. 23).
It is best not to cancel a regular, public Torah lecture at this time. Proceeding with the study will not cause participants to neglect the mitzva of bedikat ḥametz, for the search can be performed after the lesson, but canceling the lecture will result in the loss of group Torah study (SAH 431:9). After the lesson, it is good for the participants to remind each other to hurry and perform the bedikat ḥametz.