I found waking that hour earlier, eg. 3am instead of 4am made it easier to put DS back to sleep. I was more determined at 3am than 4am and DS was used to sleeping at that hour. I also eventually worked out that his body clock worked better going to bed earlier and he'd sleep longer in the morning.
Naps at 9 weeks old are pretty variable, if you're getting the night and one nap in the crib, you're doing well. Its unusual for a baby of this age to go to sleep completely on their own - often they need shush/pat after being put into the crib drowsy, often they rouse at 30 or 45min into the nap and then need shush/pat to get back to sleep. Its easiest to get them back to sleep and help them learn to make it through the sleep cycle transition if you're there when LO rouses rather than waiting til baby's screaming and upset. Sometimes white noise can help the length of nap - think how noisy a belly sounds if you put your head on someone's chest/belly - think about the constant noise of your heartbeat and your gut, etc. that LO's been listening to for almost her entire life - she's comfortable and feels safe and secure when she's on your chest.
Could well be a growth spurt, only way to get through that is to feed
Could also be pain/discomfort - gas/reflux an issue?
WRT getting up and starting the day - that depends on you. I got up at 5am but that was me, I was comfortable doing that. Others aren't. Just keep in mind that keeping it quiet and dark, not interacting with LO and keeping them relaxed and resting is an idea if you can't get them to sleep. A time is all the time from eyes open to eyes closed, so if LO is up for more than 1:15 to 1:30 at this age, they'll be OT and struggle to sleep. If you have to have LO nap out and about, a carrier/wrap or a pram can work - its more important to get the sleep than to have all naps in a cot or at a particular time.
EAS is a routine, its just a sequence of events so life is more predictable for you and baby, its not a schedule.