Ok firstly welcome to this site
There are a few things you are going to have to tackle and I know you are going to get great advice and support 'cause the mums on this site are AMAZING!!!!
Ok I think there are a few things you need to deal with:
1. 30 minute sleeps are a sign that your LO is over tired. When babies are over tired they actually rouse completely when they come into their lighter sleep cycle rather than partially rousing then going back to sleep. I would go in and watch your baby sleep for a day, observe what is happening at the 30 minutes...if she is jolting herself awake, applying gentle pressure to her legs and arms can help.
2. The first sleep in the morning is a bit of an extension of the night sleep, so often LOs will need to go down to bed earlier for this nap. Try reducing your A time by say 15 minutes and see if she goes down easier and sleeps a little longer. You will have to do this for a few days I would think to see if it helps.
3. The rocking and nursing are props for your LO. I would imagine that a lot of the wakings are probably because your LO thinks this is how to get back to sleep. There are plenty of ways to remove these props, but they are difficult, they do involve quite a lot of crying and you will have to spend a bit of time to get back on track. Basically you will need to teach your LO a new way of going to sleep and it is hard work, but OH SO WORTH IT. Don't be worried either, I put our bub to sleep in my arms for 11 MONTHS and PU/PD worked beautifully for us. To get advice for this, I would post over on the PU/PD board, Anna is wonderful over there and she will be able to explain exactly how it works and what to do...I would write it here, but it will end up as a HUGE reply and I don't want to do that to you!!! PU/PD is the answer for removing props and for training independent sleep after 4months old, so that's the way I would go.
3. You need to be very consistent with how you put your LO to bed. If you are ready for your LO to sleep in her crib it has to be the only place she sleeps while you do your sleep training...so you are going to need some time at home to get it all working (you will probably get there really quickly so don't let that put you off)...If you occasionally give in and put your LO to sleep with you or nurse to sleep during the day this will set you back a lot, it reinforces the habit. I guess what I am trying to say is you need to be certain in your own mind that you are ready...
Also you and bub are not naughty, you have done what you felt you needed to do to get yourselves through those first difficult and sleep deprived months. Don't feel guilty or worried for what you have done in the past, now you are on track to learning and teaching a better more sustainable way of sleeping, that's great....
BW is a really gentle approach and a really wonderful way of connecting with your bub, I am amazed at how well it works and the amount of help and support you get here, I love this site it's been my saviour!! I hope that this helps a little and I will try and help any way I can, even though I am still learning too
Big Hugs
lizzie