Can I play PSX/PS1 games on PS2?

[Dell]

Maybe you guys get it wrong. I mean when I insert PS1/PSX CD, I get the memory card screen (*SEE MY PREVIOUS POST*) instead of the game screen.

That means your disc is corrupt. It can't read the disc, so it boots you into the browser instead. Try resurfacing it; you can get resurfacing kits pretty cheap these days.

I can't pick up.....

The disc tray or the game disc itself?

I try to read my PS2 compatible software and:
Playstation format CD-ROMs that have the Playstation logo and the NTSC/J designation. Does this affect something?

Your disc, clearly.
You should get an error message if the region is incorrect.

Error message like what?