Yes, this was possible with the PS2. You could get a HDD adapter for the FAT PS2 models, which would accept an IDE HardDisk Drive. Then using a 3rd PArty tool, it could copy to and play games from the HardDisk.
This is also possible on the PS3 via ModChips. The Cobra ODE is one such option.
Sort of - there is the tonyhax tool that allows you to softmod an unmodified PS1.
There is a nice table on that page that shows which versions of the console it will work with.
Specifically, FreePSXBoot is probably what you are looking for - it lets you use a special memorycard with tonyhax on it to softmod the console.
Here is a video by Modern Vintage ...
Looking at the figures given, the GS by itself appears to have 40 million transistors @280 mm². That's a density about double that of the EE. This isn't unusual; CPUs are known to have a fairly low transistor density compared to other more regular chips.
But putting an extra 40 million transistors on the EE die, using the same process, would have quadrupled ...
Per the developers of PSIO, the answer is no:
Exactly why is [the internal modification] required?
There are two signals that PSIO needs in order to function that are not present on the expansion port. These are the CS (Chip Select) and INT (Interrupt) lines from the CD controller. The job of the Switch Board is to basically forward them as well as connect ...