1-disable don't show empty rows
2- Datagrid properties has a default value of 20, change per datagrid.
3- use CSS, see theme folder within your project directory.
4- This can be done by using CSS, probably you need to adjust the height and set it to fixed height?
Regarding part 4 of your question have a look at https://gettingstarted.mendixcloud.com/link/module/69/lecture/472 there you will found how you can use regions in your page template to get the desired behavior.