Hi, Welcome to the boards. Sorry you're having a tough time at the moment. Teaching your lo to sleep independently, is going to be completely different to anything he has been used to before, so it will probably take some time, and as always.. patience, persistence and consistence.
You will need to have a bedtime/naptime routine, including wind down time, when you are preparing him for what is to come. Tracy always said that sleep is a journey, not an event. Darken the room and make the enviroment comfortable.
Because your lo is able to stand, it is probably best to just do the put down part of pu/pd. A lot of babies of this age settle better out of your arms rather than in them ( although, I do still pu my lo sometimes, as for him this works). So you can see what is the best way for you.
45 mins is the average sleep cycle, which is normal, so you will need to use the same methods to change this too.
I would suggest just working on one or two areas to start with- a couple of naps or just bedtime, as it can feel a bit overwhelming to try to fix it all.
Let me know how it goes.
Cheryl