Photoshop as in the general concept of editing photos? Sure. There are a lot of decent tools out there, including for mobile devices.

Photoshop as in use the proprietary Photoshop UI? Probably not.

You can't Photoshop without Photoshop, that's the name of the software.

You can of course edit photos with whichever other software out there.

This is a web-based clone and it's all I use for photo editing.

https://www.photopea.com/

What's with the ^ and the TM letters ..

Professionals use Adobe software because it is what they know and because it is the standard. But there is no reason you need to use Photoshop unless you are working with a company that requires Photoshop.

Photoshop is just an advanced image editor made by Adobe. On Windows, Mac and Linux, GIMP is probably the most well known alternative to Photoshop. It can do roughly 99% of the things that Photoshop can do, and, more than likely, far more than you are ever likely to need. Even as a professional image editor or artist.

I'm sure that there are several options for iOS, but I don't know them by name.

Here are a couple of completely free tools to explore your goals.

Adobe's suite isn't the king it once was.

https://docs.krita.org/en/ (powerful image editing)

https://inkscape.org/learn/ (vector illustrations)

https://docs.blender.org/manual/en/latest/ (animation tool)

https://cdn.openshot.org/static/files/user-guide/index.html (video Editor)

Most of these tools are more capable than I described and there are many more foss tools out there.

Edit: just saw the iPhone part of your message. (Sorry about that) Even an old computer is capable of using most of these. You could consider running Ubuntu on one.

Try gimp first? Or blender even.

I've had Pixelmator for years and it's more than enough for my quite unprofessional editing needs. Someone with better artistic skills would be able to do pretty much all the same stuff they would do in PS from what I gather.