AE can be pretty much any size of video. 1280x720 tends to be more on the corporate side in my work. 2550x4200 (4200 x 2550?) would be fine if that fits your output. We work in so many sizes UHD, 3840 x 2160p, DCI, 4096 x 2160 and any customized sizes.FYI--The size you listed is basically portrait--like a vertical mobile device or phone. Is this correct? Once again, yes--AE can handle this. We create videos for IGTV at 1080 x 1920 and 2160 x 3840 all the time.
1. If your media is a different size than your format, you can just create your 1280 x 720 or 1920 x 1080 or ANY frame size composition and then just drag your imported Photoshop media into the new Composition. Because the Photoshop Aspect Ratio of your file may be different, just use SCALE under TRANSFORMS to re-size and crop your Photoshop file until fits the frame dimensions perfectly. SIDE NOTE: If you want to import your Photoshop and use the full 2550x4200, just DRAG the Photoshop media into the NEW COMPOSITION button to create a composition at the exact size of your media. You can always go to COMPOSITION > NEW COMPOSITION and create your composition from scratch as well.
2. If you are going to be SCALING your Photoshop media in AE--or will be using Camera(s) to fly in and out of your media in AE--vector media would be better (Note: make sure that the vector layers have the Re-Rasterize button selected to keep your vector media clean). If you remain with the Photoshop media, you should be designing much higher resolution media to prevent too many problems caused by cameras and scaling. For example, if your design is 2550x4200, I would at least design out to 5100 x 8400. While it won't be vector--you will have a better time scaling and using cameras.
3. Mockups: Your question depends on what you are mocking up. If you can do your mockups in AE that would be good. If your mockups require a lot of complex textures, etc--Photoshop would be the place to start. But, once again, it depends on what and how you wish to animate in AE. Photoshop can be extremely powerful and useful--or useless if it is something easy to accomplish in AE.