WP options plugin setting not saving the selected checkboxes

Your code just outputs empty checkboxes. You have to check each box’s value and then set checked="checked" if it’s true.

<td><input type="checkbox" placeholder="Meta Key" name="map_option_3"
    <?php // check whether map_option_3 was saved
    if(isset(get_option('map_option_3'))) { ?>checked="checked"<?php } ?>
 />Name<br>
<input type="checkbox" id="cb_name" name="map_option_4"
    <?php // check whether map_option_4 was saved
    if(isset(get_option('map_option_4'))) { ?>checked="checked"<?php } ?>
/>Price<br><input type="text" name="metakey" id="metakey" placeholder="Meta Key"></td>

You should also make name and price into actual form labels, not just plain text beside the boxes. 🙂