Screen two would be just a basic position animation. If you want all of the layers to move together, you could just parent all of them to the first one in After Effects.
Screen one would be done by scaling up and animating the opacity of the next layer from 0 to 100. Again, parenting would probably be helpful so that all of the pieces move together.
As you're new to AE, you should start here: Getting started with After Effects (CS4, CS5, CS5.5, CS6, & CC)
The zoom-through effect on screen one can get complicated. If you ecompose the Google streetview effects carefully, you will see there is a bit of implied movement that is created by the first image zooming forward while it is being slightly distorted. Image 1 dissolves away as IMage 2 comes forward in a similar way, magnification and a bit of distortion. Zoom blur works if you are going straight ahead but if the point of view is turning a corner, the type of distortion or blur must change.
Thank you a lot for such good answers!
I have combined raw data, pictures and videos for screen 1. Tomorrow I'll start to search internet how I actually can combine two 1920*1080 canvases to make it video with 3840*1080 resolution. And how to set one video track to right and second video track to left half of the canvas. My goal is to be able to export the ready project to MPEG file that in conference only needed thing is to press <full screen> and video automatically fills both screen without distortion or what's so ever. AV installation team will take care of proper screen installation but I just have to make the video file suitable for 3840*1080 resolution.
Adding sounds is no problem anymore. I've watched several tutorials to be able to say I'm somehow familiar with premiere.
My worry is that I'm running out of time. This needs to be ready by Sunday.
Three things that I need to understand so I can call this a victory:
1) how to bind two 1920*1080 video canvases together and how to separate video tracks to effect different halves of the 3840 pixel-wide canvas
2) Make the walk-through effect
3) Make the slide effect.
It's easy to make a composition in After Effects at 3840x1080 and place your two 1920x1080 compositions in it. You could do this in Premiere too with one big sequence and nest your other two sequences in it.
Getting a system that plays back video like that across two screens might be a little more tricky.
Quick and easy playback of synced comps at lower than hoped for resolution:
Place your two comps side-by-side into a single 1920x1080 comp. It will be letterboxed top and bottom and your two comps will be scaled way down to fit--can't be helped. Render.
Play this back from a single DVD or computer and feed the signal to two projectors (video splitter or HDMI repeater-hub required, far easier with simple video). Mask each projector to only show one side of the frame.