Press the loupe button to cycle between query building, query unit and look modes.
Many actions are confirmed either by pressing the green circle (OK) button, or by touching the tile with cursor again. For example, you can touch a tile twice to place a building there.
Touching the screen with two fingers is another way to show the main menu.
If you're having troubles precisely placing a building (especially for multi-tile buildings), touch the screen anywhere, hold for a sec and then move finger to move the cursor precisely.
When placing buildings, press and hold OK button to automatically select item(s) to use without displaying the item selection screeen. Likewise, when selecting a building to link to a lever or trap, press and hold OK to automatically select mechanisms to use.