The Sages prohibited starting a task or a meal during the half hour before the time of bedikat ĥametz, out of concern that one might become caught up in these activities and forget to search for ĥametz. It is permitted, however, to snack on fruit or pastry, or to perform light work that can be finished quickly.
Once the time for bedikat ĥametz 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 even begin studying Torah once the time for bedikat ĥametz has arrived. If one began studying Torah beforehand, some poskim rule that he may continue studying (Beit Yosef). Nonetheless, 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 ĥametz at its proper time (MB 431:11; Kaf Ha-ĥayim 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 ĥametz, for the search can be performed after the lesson, but canceling the lecture will result in the loss of group Torah study (SA Ha-Rav 431:9). However, the participants should remind each other after the lesson to be prompt about searching for ĥametz.