Can I modify a Google Document document table from Android or on the Web?
Yes you can do this within Google Drive/Docs app. Enter the edit mode of the document that you want to edit; tap on the cell you want to add row/column on, a hover menu will appear; then tap on the overflow menu (circled red):



A list of actions you can do on the cell will appear, scroll through the list of actions to find the ones for inserting row/columns: