No you cant softmod a ps1 theres swap disks and the 'swap trick' but we are really at another place now. The emulators are really made the way and you can find really really good emulators for PC, PSP and WII in that order. You can also play them on a softmoded ps2 but its not that easy as not all ps2 are compatible with the program.
If you are really into ps1 games what i would recommend overall is buying a used ps2 (fat are like 20$ in my country) and put a modchip in it (modbo clone 4 $ over at dealextreme) that way you for 24$ you get 100% compatiblity and a lot of extras!!!
As well as swap devices there are serial port devices (about as close to softmod/plug and play as you get with the PS1) around in some places and there are also modchips around for next to nothing: http://www.eurasia.nu/shop/default.php?cPath=52
Option2- PS1 emulation has been awesome for years now (as such requires machines considered rather wimpy by the standards of today) and PS controller to USB adapters seem to run about $5 AUD
Varies from chip to chip. I'm sure a lot require some soldering, but some may be like the Xbox and be solderless. An emulator would be your best bet. No need to burn discs, fiddle with another console etc.
Yes that's it, note that you will still need to switch that disc with the burned one and blocking the sensor. You have to do it once ever time before you put in a copied game. If you are doing it on the PS2 you will need a slidecard, or the magic keys for the ps2 slim. Breaker Pro works on PS1 games only.
You can softmod a ps1 without taking it apart all you need is a playstation code card you can buy them off ebay and amazon very cheaply.
They plug into the back of the ps1 just insert it in through the serial I/o port (the ps1 slim does not have a serial port some later ps1 consoles made before the slim don't have one either check your console before buying one.)