If I buy PureRaw, does it come with sharpening as well, or do I need PhotoLab, too?
Pureraw is to be used with other demosaicer than photolab and allows to get 2 importants things from photolab : denoising and lens corrections.
For now, last algorythm of DxO for denoising is in pureraw, photolab will get it in version 8 (the next one coming probably near end september, october).
I'm not sure I understand what Lens Correction does. Is it sharpening?
Lens corrections come from tests done on lens/cameras combinations. You'll get them only if your couple has been tested. Lot of are. There is a list of tested combinations on Dxo web site.
They are supposed to enhance the IQ results of your lens/camera models combination, when it works normally. They do not compensate problems like out of focus, motion blur or maybe the strange problem you've got one time without knowing why, when topaz tries to handle that. So don't hope to get sharper image with photolab or pureraw where image is "blurred". Instead imagine this as getting a better lens than you have for the same price.
Their modules handle sharpness (called softness I think), distorsion, aberrations, vigneting.
I would recommend to lower default value of 1 for sharpness (softness) to 0 for better starting point.
I'm not sure pureraw has as much parameters to tweak than photolab in this area.
I had a soft photo of a baby. DxO made a mess, and Nik 7 made a mess.
As I said above, photolab (or pureraw) lens corrections won't correct (sharpen) an image with a problem (out of focus, motion blur or something like this). They are supposed to get "the best" of your lens and camera combination when the shot is good.
PS: Photolab only displays most of those corrections when viewed at 75 % zoom minimum. Less than that, you can not see the preview of them. I don't know how pureraw4 manages this.