Lapidot - Rabbi Itzchak from the House of Rabi Ami: because she made the wicks for the Tabernacle. And she sat under the date palm - Rabbi Shimon be Avshalom: because of yichud. Another explanation: just as the shade of the palm tree is small, so the number of Torah scholars of her time was small. Another opinion: just as a plam tree has only one heart, so in her time Israel was of one heart with their Father in Heaven.
And she sat under a palm tree - as it is not the way of women to seclude themselves at home [with men] and so she sat in the shade of the date palm and taught Torah to the public.