Okay a few things here - firstly, its so hard the first 6 months - really, it gets easier, I found after about 6/7 months once they are on solids, their sleep particularly in the daytime, really settles. And my absolutely terrible settling son - who would SCREAM at bedtime and have me in tears myself (but be so tired there was no way he could do anything but go to bed) - now literally rolls out of my arms and into the cot - he is 1 year old now - and it's been so much better at bedtime since about 9 months I would say.
re. the naps in the day - rather than be rigid about 3pm etc, I think at that age that is expecting too much - ignore the books that tell you they must sleep at certain times. At that age they need a nap every couple of hours - so, morning, early afternoon, late afternoon - dont worry about what time, just look for the signs.
also - babies are not robots and they need cuddles to sleep - they cry because they want you close to them - that doesn't mean you have to keep them in your arms, but it does mean that sometimes when they are tired, you will have to cuddle/rock/ sing to them even though they are exhauste d- they need your help to sleep.
being a baby is hard work! their little world is so strange and confusing - they are not rational beings like us - I really reocmmend a book called the Wonder Weeks - it will explain all the changes going on in your babies brain that make them hard to settle,.
you are not going 'so wrong' as you say - she is a baby this is what they do! they are unpredictable and they do not behave like the books say they will - and it's completely normal for her to wake at night - she is tiny, none of the babies I know slept through regularly before 8/9 months - and even now aged 1, my son sometimes wakes crying for no reason....