I don't know anything about photography so I'm sorry if it's a stupid question. Can I recreate something like this
in Photoshop with a photo I took with smartphone?
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An easy way to get film looks in Photoshop is to use the Analog Efex free plugin: https://www.google.com/nikcollection/products/analog-efex-pro/ With some experimentation with different film types you should be able to get something close with minimal effort.
Alternatively, you can try matching the color and tone using levels and curves with this technique: https://www.youtube.com/watch?v=WHvfVc_8eMc You may be able to get a closer look, but it will take more fiddling.
Traditional color print has three color layers - cyan, magenta and yellow. The "old" look is caused by the fact that cyan dyes in the photographic paper deteriorate first and yellow are the most stable.
So in order to recreate this look from scratch, you would want to lighten cyans and little bit of the magentas.
If you want the pictures to really look like old faded prints, you would also need to recreate the film look (something that your examples do not have - they look digital). I would personally look for a plugin that can do that. In Photoshop, as a starting point, you can tweak the tone curve to an S-shape.