1st. Can the logo be positioned somewhere else than the middle, for example top right footer or just top right as now it does not allow to shift it anywhere than central.
2nd. The side bar widget is the same for each page and category review. Can the side bar widget be different for each page and even better for each category reviews where it takes the primary category?
1. You can change the position of the logo only with custom CSS and by changing the head template, there are no Theme Options for the position of the logo. If you need any help on how to override the header template in your child theme please let me know.
2. If you want to show certain widgets on certain pages/posts/categories/etc there are several plugins:
A few examples: