To make this a little simpler in hopes of baiting an answer, let's divide this into two parts:
109A
Because they do not usually need to make constitution checks, can constructs and undead walk over land while 'resting' to recover spells? Technically a long walk would not be physically demanding.
109B
Could a spellcaster get 'restful calm' by riding an animal somewhere? Would the rest only be interrupted by anything that demands a ride or concentration check? Would those even interrupt rest?