Okay, well, sleep training never really stops. Different things pop up along the way developmentally. But, yes, Emma slept on her own (mostly) by 3 mo at night. Other than wind-down and swaddle, she went down in her cot, talked to herself for about 20 minutes, but fell asleep on her own w/o help. During the day, she needed help sometimes, and other times she went down on her own. Mostly, like yours, the early mornings were more consistent then later in the afternoon when the day had caught up with her. That's where I was at 3 months, but I can't stress enough that every DD is different. I was doing the same as you, asking all mothers how long their babies took. I was jealous of those who only had to do it for a week, and other moms were sleep training still at 6 months... Key is just be consistent and let yours learn at her own pace.
At 2 months, where your lo is at now, was my toughest month. I was stressed b/c my DD needed to start daycare at 3 months, and I wanted her to learn independent sleep b4 daycare so she wouldn't be left to CIO (cry it out) at daycare for naps. But my routine at 2 months was eat at 7, 10, 1, 4, 6:30, DF 9:45, cross fingers and DD usually woke again at 4:30AM at night. But my naps were all over the place. It would take an hour to sh/pat, so she only napped 30 minutes before next feed and was already OT. Or, if I was lucky and she took less time to fall asleep, she would wake early from nap. Then I was like, do I feed her now? or wait? But, really, I decided to not care about the other nap issues and focused only on independent sleep. I didn't want DD to CIO at daycare nor did I want to be that parent that has to drive around the block or rock my baby to sleep when she weighed 20 pounds. Now that her independent sleep is more consistent, I'm now working on extending naps. That's why sleep training never really stops...
4 months, the routine is 4 hr EASY, and believe me, there are other issues like teething that come up. So, just when you think you got it, things change on you. Just go with the flow as issues come up and focus only on one thing at a time. You'll be less stressed and happier that way!