WHAT I WANNA KNOW ABOUT MODS.

You can but you will have to have to flash your bio's on your PS2 and install mods through transfer methods like swap disking or small mode menus flashed onto your memory card.
The xbox 360 you will have to JTAG and this will result in you not being able to play games online, I mean you can but you run the risk of having your full Live account banned and belevie me Microsoft do random sweeps all the time and ban thousand of accounts.
Alternatively you can just play the PC version of the games and install all the mods direct and even re-config the mod the files and create your own user based mods that you want (you would need to know a lot about modding though).
There is a lot of mods for the PC version of these games available.

The methods I mentioned above for the PS2 is if you want to hard mod the PS2 so it plays copies and runs the mod chip.
You will have to purchase a mod chip though.
I would suggest just tracking down "Gameshark" AR disks and using them if you want to use cheat codes.
You don't have to JUST use Gameshark there is much more company's that do these easy to use disks and all you have to do is put the disk in, select the cheats you want, replace the disk with your game of choice and start.
This is the easiest method, although if don't want to buy mod disks then you can just download them, burn them onto a disk, soft mod your PS2 so it can "swap disks" (That way it will bypass the lens restriction and recognize your disk as an official disk) and then you will be able to use your own burned version of the mod disk's.
I can provide helpful resources and videos on how to do so if you like.

*P.S - Take note that all the methods are not super fast, they may take time but some videos I can provide will give you detailed step by step instructions on how to do so.*

I see what you did there
Well if your modding the xbox then just get it JTAG'ed then.
I think you can actually get USB ones so no need for soldering or flashing the xbox's firmware (that was always a risky move)
Just plug in and download peoples mod patches and there you have it.
You should look up more info on the subject and find out how to do it, what to get and methods on getting the mods etc.

The disk's themselves can't be modified and the newer consoles need firmware modifications in order to recognise burned CD's or such devices as portable HDD, flash drives or USB drives etc.
The older consoles you could use swap disk's which where actually pretty good but in some cases don't work for certain games.
The N64 port of Resident Evil 2 was substantial watered down to support the added features of the game and for to run properly on the hardware, most enemies are missing from the game or are in locations that are easy to dodge.
The same goes for the Dreamcast version, that's why most people choose the n64 or DC version in order to do no damage knife runs or speedruns.
I do my speedruns on the original PS version or the PC port which is the same level of difficulty as the PS1 version but gives you the added "Hard mode"
I have a speedrun up on my youtube channel (search Biodeamz on youtube my profile will come up by I have no avatar, you will get the videos there)
My run would have been drastically faster if I had changed a few things and didn't forget to pick back up the valve handle when in the sewer section.
As far as I know I'm something like the second or third fastest in the world for RE2 speedrun on Normal (that is documented I mean).
All other faster runs have been using cheats or infinite ammo or using the Japanese version or PAL easy or rookie mode.
I'm planning on doing runs of every version and mode just to see if I can beat the records for them.
That sounds pretty quick but you should have documented your run with a picture of the Result screen or videoed it as should have hard evidence of run's this fast.

I'm going to go the extra mile and try to beat you time on N64 version and upload it to YouTube
You do it on normal or easy mode ?

Ah yes the mod that MartinBiohazard done for extreme hard mode which is basically a harder version of nightmare mode.
Damn I loved that mod but it was VERY challenging, impossible for some players to complete lol.

No randomiser mode was just like arranged mode but instead randomized everything everytime you done a play through.
I didn't mean to say nightmare mode for the N64 port, I meant nightmare mode for the dreamcast and PC.