Would u suggest I begin training for naps and shift her to a 2 naps routine immediately or slowly increase her A time?
Really it is up to you. Some people feel they prefer to go a bit slower and gentler and feel confident they have the patience and energy for the slower route of increasing the A time gradually, this requires a degree of winging it as you would need to decide for yourself day to day and nap to nap how to proceed. Some people like to crack right on with a new routine and get it done as quickly as possible, they tend to be people who prefer not to wing it but to have a clear plan to follow, this route can be faster but can also include more OT. It really depends on your own personality (we've all done the baby quiz but I think in these things it's often more important to look at what personality type the parent is) and what you feel most comfortable with.
Happy to support you and offer suggestions either way. Or mid way even.
What if she wakes early like 5am and can't resettle?
Is this what is happening now? Is WU any time from 5am to 7am or more often now 5am?
The next 2 days, she did have the 3rd nap but resisted sleep and cried until around 8pm (from 6pm).
During a transitional period of nap dropping it's good to have a plan in mind what to do if the CN is taken (late BT) or refused (EBT). A LO who is dropping the CN but agrees to take one will likely need a decent A time after the CN and this can push BT much later, I never plan for later than 8pm.
So based on your routine below, should I start putting her in bed at 10am and 2:30pm or how much earlier since she probably would be resisting and crying. If she skip the nap entirely, what should i do?
Again this really depends on how you want to approach it - it would be a big change to go directly to that 2 nap routine but you can, yes, or you can increase the A time slowly and move the nap out slowly. it's very rare a LO totally skips naps for long, they do eventually sleep. If you were to go all out on the routine change you'd need to dedicate time into helping her resettle using PUPD and your back rub and key phrase until (almost) the end of nap time.
Personally I tend to move things relatively quickly but without great big changes if I can avoid them.
Regarding shush pat, we tried using it from day one but it doesn't seem to soothe my baby.
It doesn't sooth all babies, often it is used as away of letting baby know you are there and they are not alone rather than it being a magical instant soothing method. The back rub and key phrase you are using are fine - great.
Should we be picking her up more? Now that she's stronger, she rolls around the cot and buries her face in the mattress and sometimes bumping her head on the side of the cot. I read that we shouldn't be picking them up when they are doing this? Even though they are still crying?
The most important aspect is that you are there and you let your LO k now you are there, by touch and voice. She needs to know she is not alone. you are doing this. Otherwise, again it is quite individual. I always picked mine up, I knew full well he would not settle until I did so even when he was fully independent for sleep and had been for a long time if he was crying he needed picking up, sometimes a very brief pick up but then he'd quickly settle back down and self sooth or calm with a hand on him. This was well beyond the age where the guidance is to not pick up - I knew I had to.
So you can find your own way with this. If she calms more quickly in your arms I'd pick her up, but if she is flailing and kicking so much you feel you could drop her then don't pick up.
Sorry, I know I am not giving you clear cut answers and that's because everyone is so individual.
I can probably offer some more suggestions when I get an idea how you'd like to proceed.