Project Properties allows for one image size (e.g. 1920x1080) for the entire project - it cannot be changed mid-project to another image size.

Media with different image sizes can still be added to the main project but will be rendered at the main project's image size. But you've got another difficulty in that 1920x1080 is 16:9 aspect ratio whereas 1280x962 is 4:3. There are usually 4 choices about how to deal with this:

1. 4:3 video in a 16:9 project will result in black bars on the L and R of the frame; but ...
2. a common trick is to copy that 4:3 video to a lower track on the timeline, in pan/crop for the media on that lower track, change the preset from 'default' to '16:9 Widescreen aspect ratio' which will increase the video to fill the width of the 16:9 aspect ratio, and then add blur to the image on the lower track and perhaps also reduce the opacity. This process results in the 4:3 image being fully displayed but instead of black bars, the L and R areas of the video is repeated on the videos outside but is softened by the blur etc; or ...
3. add the 4:3 video to the timeline and change the pan/crop preset to '16:9 Widescreen aspect ratio'. The 4:3 video will then fill the width of the 16:9 frame but the top and bottom of the 4:3 image will be chopped off. Pan/crop can be used to best frame the image vertically; or ...
4. While pan/crop is in its default preset, disable the 'lock aspect ratio' icon in the far left vertical task bar of pan/crop, and then change the preset to '16:9 Widescreen aspect ratio'. This will retain the original height of the 4:3 image but will stretch the 4:3 image horizontally to fill the width of the 16:9 frame. Whether the audience will want to watch a horizontally stretched video is a big consideration though.