The answer to both of the above questions is YES! Resting your body is just as important as working out. When you take a day off from lifting you allow your body to recover without any strain. You will optimize your recovery and it can even help you get stronger! Yes, resting can actually help you gain strength!
Yoga is a great exercise to help optimize your recovery. Whenever you stretch you're stretching your muscles out (which is why stretching after working out is so important!) allowing them to get closer to full strength quicker.
On your days off from lifting try reading a book or doing an activity that forces you to use your brain. Since we're letting our body recover we might as well work out our brain and keep it healthy to help us out when we do go back to working out!
"Don't judge my choices without understanding my reasons" - Anonymous