Practical answer - yes, but you’ll need to find out how on your own
Legal answer - no, you are pirating copyrighted software
Technical answer - buy old games from a hobby shop, buy specialist equipment to read them on your computer, and make your own copies. Perfectly legal. (ok for PS1 and PS2 you just need a DVD drive)
It feels wrong because historically, sleeping a computer during gaming was pretty likely to cause the game to freeze (or tabbing out, or doing just about anything).
Luckily it’s mostly a solved problem nowadays, I sleep during games all the time. Only game that ever gave me trouble sometimes was Assassins Creed 2 installed through Ubisoft Connect added to Steam, if I let it sleep too long it would have some kind of disconnect from Ubisoft and force close the game (even though actually playing offline was fine).
Emudeck is just a convenient installer, you have to look at the actual emulators it runs for individual games. For PS3 there is basically only one option which is RPCS3. This is also what Emudeck installs for you.
If you mean a USB flash drive, you can do it, it won’t work super well. If you just need Windows do do a specific thing occasionally it will get the job done.
That’s too new for 90s games “natively.” Windows 98 won’t be too happy on it if it runs at all.
Which Linux distro you use doesn’t matter too much, they all run the same WINE and these old games won’t be sensitive to small performance differences.
The ideal OS for these Windows games on this machine is probably Windows 7. Games will be run on a case-by-case basis as some will work fine on modern hardware/OS and some won’t. But there will often be community methods to make them work, including things like DOSBox.
The only way to get guaranteed out of the box compatibility for Windows 98 games is to run them in Windows 98 on a Windows 98-era computer. Same games just really want certain hardware.
If you can’t find a problem, don’t create one tbh.