Open details in pagebrowser

Is there any way to open details page in a page browser from a tile in a device browser?

Also, is there any way to set for example background color of a element on one page from a trigger event in an other page?

No. What you could do is have your tiles update a virtual device. Then bind the Page & Device properties on your PageBrower to the virtual device.

Not, triggers are isolated to their individual pages. They cannot change items on another page. Same as above. Use a virtual device as a bridge between the 2 pages.