Hi Steve
Now I was curious, what tool or process is used to remove hot/dead pixels?
You may use the DefectMap process that is part of the new release. Basically, you have to manipulate your image (or calibration frames, like the master dark) to create a "defect map" image, where bad pixels are signalled by a 0 value, and good pixels by 1. Then, you use this map to replace the bad pixels with different operations in that process that will exclude any bad pixels in the neightbourhood, thus yielding better results than a naive convolution (or morphological filter) and a mask.
Also, using curves and levels in PS I was always taught to do a curves adjustment and then a levels adjustment to just raise the black point followed by another curves and so on till I got the result I wanted. Is this typical of these two tools in PI and if so, can both be open at the same time and simply switch between the two? Would they share the same preview window or separate ones?
In my experience, it is better to set the black and white points as early as you can, and then leave them fixed (unless you apply some heavy noise reduction that will create unused dynamic range, specially on the dark side). Then, go to curves.
Having said that, in a side note, there a few "tricks" or "tips" that were common on PS, mainly to avoid gasping and posterization of images, due the poor bit deph of the working image (8 or 16 bits). If you use 32bits images, there is no need for such things. You may apply a very aggressive middtones transfer function (for example) to increase brightness, and then do the opposite, and there will be a minimal deterioration due to rounding errors. This is part of the new paradigm that PixInsight has been trying to incorporate into our minds since a long time ago <vbg> and one of the reasons I say that we don't need processing layers

Now into a more direct answer: yes, you may open both processes at the same time. In fact, you may open any number of processes, modify them, create icons, without a single image opened. Processes and images are living objects, they interact but do not need each other. This is the object oriented paradigm.
If you want to preview the results "live", with a RTP, make sure that the owner of the RTP is the process that you are modifying (take a look at the icon in the bottom right corner of the RTP window; to change ownership, activate the RTP buttom in the appropiate process window).