Export from Illustrator to Photoshop at a specific resolution

I got application design as .ai file, Adobe Illustrator. The design is for mobile application and I have a nice plug-in in Photoshop and Gimp that can easily export layers (and name them) to fit all mobile screens.

I read on multiple places that I have to export .ai file to .psd file. Now, the plug-in does not like up-scaling (neither do I) so I have to export AI file to PSD at a specific resolution. Let's say at 1080x1920 pixels.

How do I do that? Do I first have to resize all AI images to this resolution and then export, or this can be done automatically?

In the end, can I keep layers in PDF unrasterized or all buttons will be glued to the background?