If my newborn is really tired, should I wake him up to feed?

Yes. Newborn is usually sleepy when his/her weight is still below the birth weight. Newborn begins to cry for hunger when he/she has regained his birth-weight, and your milk supply is well established. Once he/she is gaining weight steadily, and your milk supply is well established, you can let baby feeds on demand.
Yes. I never advise waking a full term healthy infant to feed. They are hardwired to demonstrate hunger thru fussing, rooting etc.It is normal in the 1st few days of life to have very irregular feedings. After 3-4 days babies begin to choose their " schedule". At this point we expect their weight to increase. If they wet 5 or more diapers per day, they are usually ok.
Yes. I find it helpful to push baby to feed more often during the day by limiting down time to two hours. If they won't latch or feed, i keep them up for 5 min then let them nap another 1/2 hr & try again. I leave them alone at night, letting them set their next wake/feed time.This can set a good pattern in a few days. Babies often flip their day/night schedules if you let them take extended day naps.