In Photoshop, after I have pasted a selection into an image, is it possible to resize only the selection so it fits into the image?
Indeed it is..........the selection should come in as a new layer......go to that layer and "load selection".......once you have done that, you can modify the selection in a variety of ways......right click to get the options..........
to resize just one layer, select it (preferably with a marquee around it by right clicking on its preview in the layers list, this just makes sure that only that layer is resized and its good practice)
then wit it selected go
edit / transform / scale
hold down shift to keep it to scalce with itself (like you do with marquee tool and things when u want a square or even circle) then adjust away
After you have copied and pasted a part of a pic (a plane for instance) you can simply resize it by selecting the layer (layer is selected by default, just after pasting it in) and then go to edit - transform - scale, as sgt Donut said.
You can hold down shift to save the aspect ratio, also as explained by sgt Donut. Hold down alt to resize from the center instead of the corner.