I'm not sure why that's taking too long, but for one thing, you don't have to "highlight". As log as there is a live insertion point somewhere in the table, cell borders will be drag-able.
I'm wondering why you are going to the trouble of using table cells in this design. Why not simply make a paragraph style and set tabs?
But yes, unfortunately, you cannot set cell dimensions in a cell style.
I'm working on someone elses document.
Thanks for reaching out. I found a few similar discussions which you can refer to:
Please try the suggestions and let us know if this helps or if you need any further assistance.