Is there something like this that allows you to play backups of PS1 games on an unmodded PS2?
bonus question: does Cturt/FreeDVDBoot allow you to play PS2 games from other regions?
As far as I'm aware, the only way to play backups of PS1 discs is with a modchip. What you can do without a chip, however, is to play backups of PS1 games through softmods. You can play games via SMB, USB (note that the PS2 are only equipped with USB1.1, and the game performance might suffer), or, if you have a phat model, internal HDD (this is what I use, and what I would recommend), using
OPL and
POPStarter, which can be booted with wLaunchElf (only OPL is needed for PS2, but both is needed for PS1). The compatibility isn't perfect, but it runs a large number of games (see
here for a list). Instead of using the FreeDVDBoot exploit every time, you can
install FMCB onto a memory card which lets you boot homebrew from the PS2 menu.
I have no experience with this myself, but you can play PS2 backups from disc by using
ESR (note that you must patch your .isos first). This might let you play region-locked games as well, but I am not sure. I'm not sure on the compatibility here either