Is it permissible to give zakat to my poor grandfather and to meet the needs of my grandmother, who lives with an orphan child and his widowed mother, knowing that the child inherits unproductive land?

It is not permissible to give Zakat to those whose maintenance is obligatory upon the Zakat-giver. It is obligatory for a capable grandchild to provide for their poor grandfather and grandmother, as they are among those whose maintenance is obligatory upon them.

Maintenance is obligatory under two conditions: that those being provided for are poor and have no wealth, and that the provider has surplus wealth for their maintenance beyond their own and their wife's expenses. If these conditions are met, then it is not permissible for the grandchild to give their Zakat to their grandfather and grandmother.