These are great tips to help your son regulate his day/night cycles and eventually begin sleeping through the night. [name_m]Just[/name_m] to reiterate-- babies naturally wake every two hours (as do adults, actually if you track brain wave activity during sleep). All of us eventually learn to stitch these cycles together, so we sleep 2, 4, 6 then 8-10 hours in a row, naturally. We develop true 24-hr circadian rhythms and a true sleep-wake cycle. Your son’s job is to learn how to do that, and the tips above (keeping things bright & stimulating during the day, dark and soothing at night; not immediately attending to him when he awakens in the night, so he begins to self-soothe, not changing diapers at night unless they’re dirty) are great.
But for short-term survival: the amount of caffeine secreted in breastmilk is the same as your blood caffeine content (like your blood alcohol content when you drink alcohol). In other words, it’s extremely low. It’s not like a shot of espresso is delivered with each 4oz feed. So if you need caffeine to function, please try it. The caveat is that some babies might still be bothered by even that minimal amount of caffeine-- my daughter was. I switched to drinking caffeinated tea instead of coffee and she’s tolerated that just fine.
I think the old advice of ‘sleep when the baby is sleeping’ is very difficult to follow. As an adult you have those 24-hr Circadian rhythms I was talking about already deeply ingrained. It’s very hard to fall asleep for 30-45 min each time the baby sleeps around the clock. The sleep isn’t restorative and it can leave you feeling more groggy and confused.
[name_f]My[/name_f] advice instead is to put yourself on a 12-hr or so nighttime cycle. You’ll actually only sleep like 6-7 of those 12 hours. But going from roughly 10 PM to 10 AM, sleep whenever the baby is sleeping (or whenever he’s not needing to be breastfed). You’ll nap in short 1-2.5 hour bursts, probably 3-4 or them over that time period. Then, mid-morning, you get up and begin your day. Shower! Make sure you shower! It’s important for your recovery post-birth from a hygienic perspective and also for your general relaxation, well-being and alertness. Get dressed in something non-pajama-like. [name_m]Don[/name_m]'t lay in bed. Drink your tea-- even if you don’t want to try caffeine, just a nice warm cup of herbal tea will help wake you and soothe you. Eat a decent breakfast and regular lunch & dinner. If the weather is decent in the area in which you live, take your son out for short little field trips. If you need one quick afternoon nap mid-afternoon when your son sleeps, take it-- but otherwise, keep yourself on a rough 12/12 hr sleep/wake cycle.
Also, you mentioned that you would try to wake your son up after three hours during the day. We are all taught in medical school that very young babies (like your son, only 9 days old) can’t go more than four hours between feedings due to the way their livers store & release energy, etc. So at least let him go four hours before awakening him. The worry is that their blood sugar goes too low and they won’t wake up from hunger cues due to the lethargic effect this creates. However, I know personally that the doctor part of me really fought with the mom part of me over this. For my firstborn, I would really assiduously awaken him if it had been 4 hours, even in the night, until he was a month old. But the mom part of me was screaming “sweet heaven, he’s asleep! Leave him alone!” and often the mom part won out. 
But even the strict doctor part would let him go 4 hours.
