Tell us about yourself!
"One of the parts are obsolete now, no ones selling them anymore." - It would be helpful if you mentioned which one is obsolete.
Please be very careful. That looks like an open switch-mode power supply. In an open switch-mode power supply, Dangerous mains voltages will be accessible and if you touch the wrong place you could receive a fatal electric shock. Please be very careful. I think you'd be much safer using an enclosed power supply as suggested in the instructable. The very-same voltages are present, but should stay safely enclosed within the casing.
I rather suspect that you may need a fan for the version with the small heatsinks, especially if you're dissipating more power. I found at least three variants, there may be more.
Use a solder sucker and or desolder braid. It's probably best to reflow the solder pads with lead-solder first as the lead-free type can present problems.
Why do you need a current adjustment ?Because a number of types of loads (a load is anything that you might want to power from this), rely upon a current limit. Example: LEDsLeds need a current limit otherwise the current will rise to a level at which they will be destroyed.
Linear, because the trimpots will be linear.