Can all PSP be modded?

Unfortunately, Sony has had other plans for their handheld, and has released dozens of firmware updates and several hardware revisions to make it harder to hack the PSPs handheld. As such, there's no one hack that works on all PSP, and in fact some PSPs are completely unhackable.

Is it illegal to mod a PSP?

Let's start with the easy question: it's definitely not illegal to hack your PSP, whether that means you want to take a diamond-tipped drill and put small holes in the screen or whether you want to push it in directions that the developers didn't intend, even running programs not officially endorsed by Sony Corporation ...